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Home Code Solutions Hackerrank Algorithms

Counting Road Networks – HackerRank Solution

Counting Road Networks - HackerRank Solution Java , Python 3, Python 2 , C , C++, Best and Optimal Solutions , All you need.

bhautik bhalala by bhautik bhalala
May 31, 2022
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Table of Contents

  • Counting Road Networks – HackerRank Solution Java , Python 3, Python 2 , C , C++, Best and Optimal Solutions , All you need.
  • Solutions of Algorithms Data Structures Hard HackerRank:
    • Here are all the Solutions of Hard , Advanced , Expert Algorithms of Data Structure of Hacker Rank , Leave a comment for similar posts
  • C++ Counting Road Networks HackerRank Solution
  • Java Counting Road Networks HackerRank Solution
    • Warmup Implementation Strings Sorting Search Graph Theory Greedy Dynamic Programming Constructive Algorithms Bit Manipulation Recursion Game Theory NP Complete Debugging
    • Leave a comment below
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Counting Road Networks – HackerRank Solution Java , Python 3, Python 2 , C , C++, Best and Optimal Solutions , All you need.

Solutions of Algorithms Data Structures Hard HackerRank:

Here are all the Solutions of Hard , Advanced , Expert Algorithms of Data Structure of Hacker Rank , Leave a comment for similar posts

C++ Counting Road Networks HackerRank Solution


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#include<bits/stdc++.h>
using namespace std;
typedef long long num;
typedef vector<num> poly;
const num p=663224321;
 
num pm(num a,num n=p-2,num m=p){
	num r=1;
	for(;n;n>>=1,a=a*a%m)
		if(n&1)r=r*a%m;
	return r;
}
 
struct NTT{
	static const int g=3;
	void go(num *a,size_t n){
		size_t l,b,i,s;
		num d=pm(g,(p-1)/n,p),w,t;
		for(b=n>>1,l=n;b;b>>=1,l>>=1,d=d*d%p)
		for(w=1,s=0;s<b;++s,w=w*d%p)
		for(i=s;i<n;i+=l){
			a[i|b]=(a[i]-(t=a[i|b]))*w%p;
			a[i]=(a[i]+t)%p;
		}
	}
	void back(num *a,size_t n){
		size_t l,b,i,s;
		num d=pm(n,p-2,p),w,t;
		for(i=0;i<n;++i)a[i]=a[i]*d%p;
		for(b=1,l=2;b<n;b<<=1,l<<=1)
		for(d=pm(g,p-1-(p-1)/l,p),w=1,s=0;s<b;++s,w=w*d%p)
		for(i=s;i<n;i+=l){
			t=a[i|b]*w;
			a[i|b]=(a[i]-t)%p;
			a[i]=(a[i]+t)%p;
		}
	}
}ntt;

void sqr(poly& a){
	int n=1,m=a.size();
	for(;n<a.size()*2-1;n<<=1);
	a.resize(n,0);
	ntt.go(&a[0],n);
	for(int i=0;i<n;++i)a[i]=a[i]*a[i]%p;
	ntt.back(&a[0],n);
	a.resize(m*2-1);
}
poly mul(poly a,poly b){
	int n=1,l=a.size()+b.size()-1;
	for(;n<l;n<<=1);
	a.resize(n,0);b.resize(n,0);
	ntt.go(&a[0],n);
	ntt.go(&b[0],n);
	for(int i=0;i<n;++i)a[i]=a[i]*b[i]%p;
	ntt.back(&a[0],n);
	a.resize(l);
	return a;
}
 
poly invM(poly f,int m){
	poly g;int n=1;
	g.push_back(pm(f[0]));
	for(;n<m;){
		n<<=1;
		poly t=g;sqr(t);
		for(auto&x:g)x=(x<<1)%p;
		t=mul(poly(f.begin(),min(f.begin()+n,f.end())),t);
		g.resize(n,0);
		for(int i=0;i<n && i<t.size();++i)g[i]=(g[i]-t[i])%p;
	}
	return poly(g.begin(),g.begin()+m);
}

poly h,g,invG,f;

// comb
#define MAX 300005
#define MOD 663224321
#define ll long long
ll fact[MAX],inverse[MAX],fact_inverse[MAX];

void precalc()
{
	fact[0]=1;
	
	inverse[0]=1;inverse[1]=1;
	
	fact_inverse[0]=1;fact_inverse[1]=1;
	
	for(ll i=1;i<MAX;i++)
		fact[i]=(i*fact[i-1])%MOD;
		
	for(ll i=2;i<MAX;i++)
	{
		inverse[i]=(MOD-((MOD/i) * inverse[MOD % i])%MOD)%MOD;
		fact_inverse[i]=(inverse[i]*fact_inverse[i-1])%MOD;
	}
}
// ENDS

int main(){
	precalc();
	
	int lim=5+(1e5);
	h.resize(lim);g.resize(lim);
	for(int i=0;i<lim;i++){
		h[i]=pm(2,(i*1LL*(i-1))/2);
		h[i]*=fact_inverse[i];
		h[i]%=p;
		
		g[i]=h[i];
		h[i]=i*h[i]%p;
	}
	
	invG=invM(g,lim);
	f=mul(h,invG);
	
	for(int i=1;i<f.size();i++){
		f[i]*=fact[i-1];
		f[i]%=p;
		if(f[i]<0) f[i]+=p;
	}
	
	#define sd(x) scanf("%d",&x)
	int q;sd(q);
	while(q--){
		int n;sd(n);
		printf("%lld\n",f[n]);
	}
}

Java Counting Road Networks HackerRank Solution


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import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = 100005;
		long[] a = new long[n];
		int mod = 663224321;
		for(int i = 0;i < n;i++){
			a[i] = pow(2, (long)i*(i-1)/2, mod);
		}
		int[][] fif = enumFIF(100005, mod);
		long[] ta = transformLogarithmically(a, fif);
		for(int Q = ni();Q > 0;Q--){
			out.println(ta[ni()]);
		}
	}
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}
	
	public static int mod = 663224321;
	public static int G = 3;
	
	public static long[] mul(long[] a, long[] b)
	{
		return Arrays.copyOf(convoluteSimply(a, b, mod, G), a.length+b.length-1);
	}
	
	public static long[] mul(long[] a, long[] b, int lim)
	{
		return Arrays.copyOf(convoluteSimply(a, b, mod, G), lim);
	}
	
	public static long[] mulnaive(long[] a, long[] b)
	{
		long[] c = new long[a.length+b.length-1];
		long big = 8L*mod*mod;
		for(int i = 0;i < a.length;i++){
			for(int j = 0;j < b.length;j++){
				c[i+j] += a[i]*b[j];
				if(c[i+j] >= big)c[i+j] -= big;
			}
		}
		for(int i = 0;i < c.length;i++)c[i] %= mod;
		return c;
	}
	
	public static long[] mulnaive(long[] a, long[] b, int lim)
	{
		long[] c = new long[lim];
		long big = 8L*mod*mod;
		for(int i = 0;i < a.length;i++){
			for(int j = 0;j < b.length && i+j < lim;j++){
				c[i+j] += a[i]*b[j];
				if(c[i+j] >= big)c[i+j] -= big;
			}
		}
		for(int i = 0;i < c.length;i++)c[i] %= mod;
		return c;
	}
	
	public static long[] add(long[] a, long[] b)
	{
		long[] c = new long[Math.max(a.length, b.length)];
		for(int i = 0;i < a.length;i++)c[i] += a[i];
		for(int i = 0;i < b.length;i++)c[i] += b[i];
		for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
		return c;
	}
	
	public static long[] add(long[] a, long[] b, int lim)
	{
		long[] c = new long[lim];
		for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
		for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i];
		for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
		return c;
	}
	
	public static long[] sub(long[] a, long[] b)
	{
		long[] c = new long[Math.max(a.length, b.length)];
		for(int i = 0;i < a.length;i++)c[i] += a[i];
		for(int i = 0;i < b.length;i++)c[i] -= b[i];
		for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
		return c;
	}
	
	public static long[] sub(long[] a, long[] b, int lim)
	{
		long[] c = new long[lim];
		for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
		for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i];
		for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
		return c;
	}
	
	// F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x)
	// if want p-destructive, comment out flipping p just before returning.
	public static long[] inv(long[] p)
	{
		int n = p.length;
		long[] f = {invl(p[0], mod)};
		for(int i = 0;i < p.length;i++){
			if(p[i] == 0)continue;
			p[i] = mod-p[i];
		}
		for(int i = 1;i < 2*n;i*=2){
			long[] f2 = mul(f, f, Math.min(n, 2*i));
			long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i));
			for(int j = 0;j < f.length;j++){
				f2p[j] += 2L*f[j];
				if(f2p[j] >= mod)f2p[j] -= mod;
				if(f2p[j] >= mod)f2p[j] -= mod;
			}
			f = f2p;
		}
		for(int i = 0;i < p.length;i++){
			if(p[i] == 0)continue;
			p[i] = mod-p[i];
		}
		return f;
	}
	
	// differentiate	
	public static long[] d(long[] p)
	{
		long[] q = new long[p.length];
		for(int i = 0;i < p.length-1;i++){
			q[i] = p[i+1] * (i+1) % mod;
		}
		return q;
	}
	
	// integrate
	public static long[] i(long[] p)
	{
		long[] q = new long[p.length];
		for(int i = 0;i < p.length-1;i++){
			q[i+1] = p[i] * invl(i+1, mod) % mod;
		}
		return q;
	}
	
	// F_{t+1}(x) = F_t(x)-(ln F_t(x) - P(x)) * F_t(x)
	public static long[] exp(long[] p)
	{
		int n = p.length;
		long[] f = {p[0]};
		for(int i = 1;i < 2*n;i*=2){
			long[] ii = ln(f);
			long[] sub = sub(ii, p, Math.min(n, 2*i));
			if(--sub[0] < 0)sub[0] += mod;
			for(int j = 0;j < 2*i && j < n;j++){
				sub[j] = mod-sub[j];
				if(sub[j] == mod)sub[j] = 0;
			}
			f = mul(sub, f, Math.min(n, 2*i));
//			f = sub(f, mul(sub(ii, p, 2*i), f, 2*i));
		}
		return f;
	}
	
	// \int f'(x)/f(x) dx
	public static long[] ln(long[] f)
	{
		long[] ret = i(mul(d(f), inv(f)));
		ret[0] = f[0];
		return ret;
	}
	
	// ln F(x) - k ln P(x) = 0
	public static long[] pow(long[] p, int K)
	{
		int n = p.length;
		long[] lnp = ln(p);
		for(int i = 1;i < lnp.length;i++)lnp[i] = lnp[i] * K % mod;
		lnp[0] = pow(p[0], K, mod); // go well for some reason
		return exp(Arrays.copyOf(lnp, n));
	}
	
	// destructive
	public static long[] divf(long[] a, int[][] fif)
	{
		for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[1][i] % mod;
		return a;
	}
	
	// destructive
	public static long[] mulf(long[] a, int[][] fif)
	{
		for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[0][i] % mod;
		return a;
	}
	
	public static long[] transformExponentially(long[] a, int[][] fif)
	{
		return mulf(exp(divf(Arrays.copyOf(a, a.length), fif)), fif);
	}
	
	public static long[] transformLogarithmically(long[] a, int[][] fif)
	{
		return mulf(Arrays.copyOf(ln(divf(Arrays.copyOf(a, a.length), fif)), a.length), fif);
	}
	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}
	
	public static long[] reverse(long[] p)
	{
		long[] ret = new long[p.length];
		for(int i = 0;i < p.length;i++){
			ret[i] = p[p.length-1-i];
		}
		return ret;
	}
	
	public static long[] reverse(long[] p, int lim)
	{
		long[] ret = new long[lim];
		for(int i = 0;i < lim && i < p.length;i++){
			ret[i] = p[p.length-1-i];
		}
		return ret;
	}
	
	// [quotient, remainder]
	// remainder can be empty.
	// @see http://www.dis.uniroma1.it/~sankowski/lecture4.pdf
	public static long[][] div(long[] p, long[] q)
	{
		if(p.length < q.length)return new long[][]{new long[0], Arrays.copyOf(p, p.length)};
		long[] rp = reverse(p, p.length-q.length+1);
		long[] rq = reverse(q, p.length-q.length+1);
		long[] rd = mul(rp, inv(rq), p.length-q.length+1);
		long[] d = reverse(rd, p.length-q.length+1);
		long[] r = sub(p, mul(d, q, q.length-1), q.length-1);
		return new long[][]{d, r};
	}

	public static long[] substitute(long[] p, long[] xs)
	{
		return descendProductTree(p, buildProductTree(xs));
	}
	
	public static long[][] buildProductTree(long[] xs)
	{
		int m = Integer.highestOneBit(xs.length)*4;
		long[][] ms = new long[m][];
		for(int i = 0;i < xs.length;i++){
			ms[m/2+i] = new long[]{mod-xs[i], 1};
		}
		for(int i = m/2-1;i >= 1;i--){
			if(ms[2*i] == null){
				ms[i] = null;
			}else if(ms[2*i+1] == null){
				ms[i] = ms[2*i];
			}else{
				ms[i] = mul(ms[2*i], ms[2*i+1]);
			}
		}
		return ms;
	}
	
	public static long[] descendProductTree(long[] p, long[][] pt)
	{
		long[] rets = new long[pt[1].length-1];
		dfs(p, pt, 1, rets);
		return rets;
	}
	
	private static void dfs(long[] p, long[][] pt, int cur, long[] rets)
	{
		if(pt[cur] == null)return;
		if(cur >= pt.length/2){
			rets[cur-pt.length/2] = p[0];
		}else{
			// F = q1X+r1
			// F = q2Y+r2
			
			if(p.length >= 1500){
				if(pt[2*cur+1] != null){
					long[][] qr0 = div(p, pt[2*cur]);
					dfs(qr0[1], pt, cur*2, rets);
					long[][] qr1 = div(p, pt[2*cur+1]);
					dfs(qr1[1], pt, cur*2+1, rets);
				}else if(pt[2*cur] != null){
					long[] nex = cur == 1 ? div(p, pt[2*cur])[1] : p;
					dfs(nex, pt, cur*2, rets);
				}
			}else{
				if(pt[2*cur+1] != null){
					dfs(modnaive(p, pt[2*cur]), pt, cur*2, rets);
					dfs(modnaive(p, pt[2*cur+1]), pt, cur*2+1, rets);
				}else if(pt[2*cur] != null){
					long[] nex = cur == 1 ? modnaive(p, pt[2*cur]) : p;
					dfs(nex, pt, cur*2, rets);
				}
			}
		}
	}
	
	
	public static long[][] divnaive(long[] a, long[] b)
	{
		int n = a.length, m = b.length;
		if(n-m+1 <= 0)return new long[][]{new long[0], Arrays.copyOf(a, n)};
		long[] r = Arrays.copyOf(a, n);
		long[] q = new long[n-m+1];
		long ib = invl(b[m-1], mod);
		for(int i = n-1;i >= m-1;i--){
			long x = ib * r[i] % mod;
			q[i-(m-1)] = x;
			for(int j = m-1;j >= 0;j--){
				r[i+j-(m-1)] -= b[j]*x;
				r[i+j-(m-1)] %= mod;
				if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
//				r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
			}
		}
		return new long[][]{q, Arrays.copyOf(r, m-1)};
	}
	
	public static long[] modnaive(long[] a, long[] b)
	{
		int n = a.length, m = b.length;
		if(n-m+1 <= 0)return a;
		long[] r = Arrays.copyOf(a, n);
		long ib = invl(b[m-1], mod);
		for(int i = n-1;i >= m-1;i--){
			long x = ib * r[i] % mod;
			for(int j = m-1;j >= 0;j--){
				r[i+j-(m-1)] -= b[j]*x;
				r[i+j-(m-1)] %= mod;
				if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
//				r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
			}
		}
		return Arrays.copyOf(r, m-1);
	}

	public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
	public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
//	public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033};
//	public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};
	
	public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
	{
		int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
		long[] fa = nttmb(a, m, false, P, g);
		long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
		for(int i = 0;i < m;i++){
			fa[i] = fa[i]*fb[i]%P;
		}
		return nttmb(fa, m, true, P, g);
	}
	
	public static long[] convolute(long[] a, long[] b)
	{
		int USE = 2;
		int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
		long[][] fs = new long[USE][];
		for(int k = 0;k < USE;k++){
			int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
			long[] fa = nttmb(a, m, false, P, g);
			long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
			for(int i = 0;i < m;i++){
				fa[i] = fa[i]*fb[i]%P;
			}
			fs[k] = nttmb(fa, m, true, P, g);
		}
		
		int[] mods = Arrays.copyOf(NTTPrimes, USE);
		long[] gammas = garnerPrepare(mods);
		int[] buf = new int[USE];
		for(int i = 0;i < fs[0].length;i++){
			for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
			long[] res = garnerBatch(buf, mods, gammas);
			long ret = 0;
			for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j];
			fs[0][i] = ret;
		}
		return fs[0];
	}
	
	public static long[] convolute(long[] a, long[] b, int USE, int mod)
	{
		int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
		long[][] fs = new long[USE][];
		for(int k = 0;k < USE;k++){
			int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
			long[] fa = nttmb(a, m, false, P, g);
			long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
			for(int i = 0;i < m;i++){
				fa[i] = fa[i]*fb[i]%P;
			}
			fs[k] = nttmb(fa, m, true, P, g);
		}
		
		int[] mods = Arrays.copyOf(NTTPrimes, USE);
		long[] gammas = garnerPrepare(mods);
		int[] buf = new int[USE];
		for(int i = 0;i < fs[0].length;i++){
			for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
			long[] res = garnerBatch(buf, mods, gammas);
			long ret = 0;
			for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod;
			fs[0][i] = ret;
		}
		return fs[0];
	}
	
	// static int[] wws = new int[270000]; // outer faster
	
	// Modifed Montgomery + Barrett
	private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
	{
		long[] dst = Arrays.copyOf(src, n);
		
		int h = Integer.numberOfTrailingZeros(n);
		long K = Integer.highestOneBit(P)<<1;
		int H = Long.numberOfTrailingZeros(K)*2;
		long M = K*K/P;
		
		int[] wws = new int[1<<h-1];
		long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
		long w = (1L<<32)%P;
		for(int k = 0;k < 1<<h-1;k++){
			wws[k] = (int)w;
			w = modh(w*dw, M, H, P);
		}
		long J = invl(P, 1L<<32);
		for(int i = 0;i < h;i++){
			for(int j = 0;j < 1<<i;j++){
				for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
					long u = (dst[s] - dst[t] + 2*P)*wws[k];
					dst[s] += dst[t];
					if(dst[s] >= 2*P)dst[s] -= 2*P;
//					long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
					long Q = (u<<32)*J>>>32;
					dst[t] = (u>>>32)-(Q*P>>>32)+P;
				}
			}
			if(i < h-1){
				for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
			}
		}
		for(int i = 0;i < n;i++){
			if(dst[i] >= P)dst[i] -= P;
		}
		for(int i = 0;i < n;i++){
			int rev = Integer.reverse(i)>>>-h;
			if(i < rev){
				long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
			}
		}
		
		if(inverse){
			long in = invl(n, P);
			for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
		}
		
		return dst;
	}
	
	static final long mask = (1L<<31)-1;
	
	public static long modh(long a, long M, int h, int mod)
	{
		long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
		return r < mod ? r : r-mod;
	}
	
	private static long[] garnerPrepare(int[] m)
	{
		int n = m.length;
		assert n == m.length;
		if(n == 0)return new long[0];
		long[] gamma = new long[n];
		for(int k = 1;k < n;k++){
			long prod = 1;
			for(int i = 0;i < k;i++){
				prod = prod * m[i] % m[k];
			}
			gamma[k] = invl(prod, m[k]);
		}
		return gamma;
	}
	
	private static long[] garnerBatch(int[] u, int[] m, long[] gamma)
	{
		int n = u.length;
		assert n == m.length;
		long[] v = new long[n];
		v[0] = u[0];
		for(int k = 1;k < n;k++){
			long temp = v[k-1];
			for(int j = k-2;j >= 0;j--){
				temp = (temp * m[j] + v[j]) % m[k];
			}
			v[k] = (u[k] - temp) * gamma[k] % m[k];
			if(v[k] < 0)v[k] += m[k];
		}
		return v;
	}
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}

 




 

 

Warmup
Implementation
Strings
Sorting
Search
Graph Theory
Greedy
Dynamic Programming
Constructive Algorithms
Bit Manipulation
Recursion
Game Theory
NP Complete
Debugging

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