#943624 (Java21) No.2605 Pickup Parentheses

提出ソース
結果

問題	No.2605 Pickup Parentheses
ユーザー	uwi
提出日時	2024-01-12 22:47:01
言語	Java21 (openjdk 21)
結果	RE
実行時間	-
コード長	27,165 bytes
コンパイル時間	5,739 ms
コンパイル使用メモリ	94,760 KB
実行使用メモリ	84,716 KB
最終ジャッジ日時	2024-09-27 23:33:09
合計ジャッジ時間	29,826 ms
ジャッジサーバーID （参考情報）	judge3 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	86 ms 53,668 KB
testcase_01	AC	86 ms 53,608 KB
testcase_02	AC	88 ms 53,648 KB
testcase_03	AC	132 ms 54,672 KB
testcase_04	AC	130 ms 54,840 KB
testcase_05	AC	145 ms 54,780 KB
testcase_06	AC	152 ms 55,272 KB
testcase_07	AC	147 ms 55,020 KB
testcase_08	AC	160 ms 54,928 KB
testcase_09	AC	116 ms 54,092 KB
testcase_10	AC	146 ms 55,288 KB
testcase_11	AC	125 ms 54,532 KB
testcase_12	AC	99 ms 53,576 KB
testcase_13	AC	91 ms 53,656 KB
testcase_14	AC	111 ms 54,156 KB
testcase_15	AC	125 ms 54,564 KB
testcase_16	AC	97 ms 53,592 KB
testcase_17	AC	116 ms 54,352 KB
testcase_18	AC	634 ms 74,484 KB
testcase_19	AC	567 ms 68,440 KB
testcase_20	AC	247 ms 60,168 KB
testcase_21	AC	203 ms 58,996 KB
testcase_22	AC	138 ms 57,056 KB
testcase_23	AC	621 ms 74,356 KB
testcase_24	AC	257 ms 59,152 KB
testcase_25	AC	664 ms 76,084 KB
testcase_26	AC	675 ms 70,612 KB
testcase_27	AC	620 ms 72,668 KB
testcase_28	AC	63 ms 51,032 KB
testcase_29	AC	271 ms 60,684 KB
testcase_30	AC	419 ms 67,928 KB
testcase_31	AC	67 ms 50,828 KB
testcase_32	AC	67 ms 51,004 KB
testcase_33	AC	642 ms 70,716 KB
testcase_34	AC	67 ms 50,820 KB
testcase_35	AC	64 ms 50,580 KB
testcase_36	AC	62 ms 50,788 KB
testcase_37	AC	487 ms 70,336 KB
testcase_38	AC	287 ms 65,824 KB
testcase_39	AC	203 ms 63,912 KB
testcase_40	AC	427 ms 73,500 KB
testcase_41	AC	400 ms 73,160 KB
testcase_42	AC	501 ms 77,152 KB
testcase_43	AC	257 ms 66,408 KB
testcase_44	AC	249 ms 66,116 KB
testcase_45	AC	93 ms 53,444 KB
testcase_46	AC	190 ms 60,612 KB
testcase_47	AC	92 ms 53,604 KB
testcase_48	AC	97 ms 53,812 KB
testcase_49	AC	387 ms 68,824 KB
testcase_50	AC	261 ms 64,236 KB
testcase_51	AC	66 ms 50,972 KB
testcase_52	AC	308 ms 67,616 KB
testcase_53	AC	392 ms 68,072 KB
testcase_54	AC	261 ms 66,364 KB
testcase_55	AC	302 ms 68,036 KB
testcase_56	AC	189 ms 60,508 KB
testcase_57	AC	66 ms 51,024 KB
testcase_58	AC	1,058 ms 84,696 KB
testcase_59	AC	679 ms 75,240 KB
testcase_60	AC	757 ms 78,612 KB
testcase_61	AC	739 ms 76,424 KB
testcase_62	AC	854 ms 75,732 KB
testcase_63	AC	713 ms 76,336 KB
testcase_64	AC	772 ms 78,908 KB
testcase_65	AC	662 ms 79,852 KB
testcase_66	AC	1,224 ms 84,716 KB
testcase_67	AC	693 ms 75,208 KB
testcase_68	RE	-
testcase_69	AC	67 ms 50,932 KB
testcase_70	RE	-
権限があれば一括ダウンロードができます
ソースコード

raw source code
package no2xxx;

import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class No2605 {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	public void solve()
	{
		// 2236
		int n = ni(), m = ni();
		if(n % 2 == 1){
			out.println(0);
			return;
		}
		int[][] lr = nmi(m, 2);
		List<long[]> ps = new ArrayList<>();
		int[][] fif = enumFIF(200000, mod);
		for(int[] u : lr){
			if((u[1] - u[0] + 1) % 2 == 0){
				int len = (u[1] - u[0] + 1);
				long c = catalan(len, mod, fif);
				long[] p = new long[len+1];
				p[len] = mod - c;
				p[0] = 1;
				ps.add(p);
			}
		}
		long[] pm = mulAll(ps);
		long ans = 0;
		for(int i = 0;i < pm.length;i++){
			ans += pm[i] * catalan(n-i, mod, fif);
			ans %= mod;
		}
		out.println(ans);
	}

	static long catalan(int n, int mod, int[][] fif) {
		if(n % 2 == 1)return 0;
		n /= 2;
		return C(2*n, n, mod, fif) * invl(n+1, mod) % mod;
	}

	public static final int mod = 998244353;
	public static final int G = 3;

	// only 998244353
	public static long[] mul(long[] a, long[] b)
	{
		if(a.length == 0 && b.length == 0)return new long[0];
		if(a.length + b.length >= 300) {
			return Arrays.copyOf(NTTStockham998244353.convolve(a, b), a.length + b.length - 1);
		}else{
			return mulnaive(a, b);
		}
	}

	public static long[] mul(long[] a, long[] b, int lim)
	{
		if(a.length + b.length >= 300) {
			return Arrays.copyOf(NTTStockham998244353.convolve(a, b), lim);
		}else{
			return mulnaive(a, b, lim);
		}
	}

//	public static final int mod = 1000000007;
//	public static long[] mul(long[] a, long[] b)
//	{
//		if(Math.max(a.length, b.length) >= 3000){
//			return Arrays.copyOf(NTTCRT.convolve(a, b, 3, mod), a.length+b.length-1);
//		}else{
//			return mulnaive(a, b);
//		}
//	}

//	public static long[] mul(long[] a, long[] b, int lim)
//	{
//		if(Math.max(a.length, b.length) >= 3000){
//			return Arrays.copyOf(NTTCRT.convolve(a, b, 3, mod), lim);
//		}else{
//			return mulnaive(a, b, lim);
//		}
//	}

	public static final long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod;

	public static long[] mulnaive(long[] a, long[] b)
	{
		long[] c = new long[a.length+b.length-1];
		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];
		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[] mul_(long[] a, long k)
	{
		for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;
		return a;
	}

	public static long[] mul(long[] a, long k)
	{
		a = Arrays.copyOf(a, a.length);
		for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;
		return a;
	}

	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;
	}

	public static long[] truncateTrailingZeros(long[] a)
	{
		int tz = trailingZeros(a);
		if(tz == 0)return a;
		return Arrays.copyOfRange(a, tz, a.length);
	}


	public static long[] strip(long[] a)
	{
		int i;
		for(i = a.length-1;i > 0 && a[i] == 0;i--);
		if(i + 1 == a.length)return a;
		return Arrays.copyOf(a, i+1);
	}

	public static long[] lshift(long[] a, int x)
	{
		long[] b = new long[a.length];
		if (a.length - x >= 0) System.arraycopy(a, x, b, 0, a.length - x);
		return b;
	}

	public static long[] rshift(long[] a, int x)
	{
		long[] b = new long[a.length];
		if (a.length - x >= 0) System.arraycopy(a, 0, b, x, a.length - x);
		return b;
	}

	///////////////////// 基本操作ここまで

	// 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;
	}

	static long[] exp(long[] a) { return exp(a, a.length); }

	/**
	 * https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf
	 * @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series
	 * @param a
	 * @param lim
	 * @return
	 */
	static long[] exp(long[] a, int lim)
	{
		long[] F = {1L};
		long[] G = {1L};
		long[] da = d(a);
		for(int m = 1;;m *= 2) {
			long[] G2 = mul(G, G, m);
			G = sub(mul_(G, 2), mul(F, G2, m));
			long[] Q = Arrays.copyOf(da, m-1);
			long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m-1)));
			F = mul(F, add(new long[] {1}, sub(Arrays.copyOf(a, m), i(W))), m);
			if(m >= lim)break;
		}
		return Arrays.copyOf(F, lim);
	}

	// \int f'(x)/f(x) dx
	public static long[] ln(long[] f)
	{
		return i(mul(d(f), inv(f)));
	}

	// ln F(x) - k ln P(x) = 0
	public static long[] pow(long[] p, long K)
	{
		int n = p.length;
		int tz = trailingZeros(p);
		if((long)tz*K >= n)return new long[n];
		long[] pa = Arrays.copyOfRange(p, tz, n);
		int m = pa.length;

		// pa[0] must be 1
		long base = pa[0];
		long scale = invl(base, mod);
		for(int i = 0;i < m;i++)pa[i] = pa[i] * scale % mod;

		long[] lnp = Arrays.copyOf(ln(pa), m);
		for(int i = 0;i < m;i++)lnp[i] = lnp[i] * K % mod;
		long[] reta = exp(lnp);

		long kscale = pow(base, K, mod);
		for(int i = 0;i < m;i++)reta[i] = reta[i] * kscale % mod;

		long[] ret = new long[n];
		System.arraycopy(reta, 0, ret, (int)(tz*K), (int)(n-tz*K));
		return ret;
	}

	public static int trailingZeros(long[] a)
	{
		int ret = 0;
		for(long v : a) {
			v %= mod;
			if(v != 0)break;
			ret++;
		}
		return ret;
	}

	public static long[] pow(long[] P, int n, int m)
	{
		long[] PP = truncateTrailingZeros(P);
		if(PP.length == P.length)return powCore(P, n, m);
		assert n >= 0;
		long[] res = powCore(PP, n, m);
		long[] ret = new long[m+1];
		for(int i = 0, j = (P.length - PP.length) * n;j <= m;i++,j++)ret[j] = res[i];
		return ret;
	}

	/**
	 * P(x)^nをm次まで求める。
	 *
	 * Q(x)=P(x)^nとすると、
	 * Q'(x)=nP'(x)P(x)^{n-1}である。したがって、
	 * Q(x) = P(x) * Q'(x)/n/P'(x)
	 * nP'(x)Q(x) = P(x)Q'(x)である。
	 * これのx^iの係数は、
	 * n(sum_j (i-j+1)p[i-j+1]*q[j]) = sum_j p[i-j]*(j+1)q[j+1]
	 * となる。
	 * ここから、
	 * q[i+1] = (n(sum_j (i-j+1)p[i-j+1]*q[j]) - sum_{j=0}^{i-1} p[i-j]*(j+1)q[j+1]) / p[0] / (i+1)
	 * が導かれる。sumは、iが大きくなっても|P|で抑えられるので、全体でO(|P|m)になる。
	 * 0<=i-j+1<|P| -> i+1-|P|<j<=i+1
	 *
	 * またこれはnが負のときでも成立する。
	 *
	 * @param P P[0] != 0
	 * @param n
	 * @param m
	 * @return
	 */
	public static long[] powCore(long[] P, int n, int m)
	{
		long[] Q = new long[m+1];
		long ip0 = invl(P[0], mod);
		Q[0] = n >= 0 ? pow(P[0], n, mod) : pow(ip0, n, mod);
		for(int i = 0;i < m;i++){
			long s = 0;
			for(int j = Math.max(0, i+1-P.length+1);j <= i;j++){
				s += (i-j+1) * P[i-j+1] % mod * Q[j];
				if(s >= big)s -= big;
			}
			s %= mod;
			long t = 0;
			for(int j = Math.max(0, i-P.length+1);j <= i-1;j++){
				t += (j+1) * P[i-j] % mod * Q[j+1];
				if(t >= big)t -= big;
			}
			t %= mod;
			s = (s*n-t) % mod;
			if(s < 0)s += mod;
			Q[i+1] = s * ip0 % mod * invl(i+1, mod) % mod;
		}
		return Q;
	}

	/**
	 * Pがsparseな場合のP^nをm次まで
	 * O(|P|m).
	 * NOT VERIFIED
	 *
	 * @param P [index, value] P[0] != 0
	 * @param n
	 * @param m
	 * @return
	 */
	public static long[] pow(long[][] P, int n, int m)
	{
		long[] Q = new long[m+1];
		long p0 = 0;
		for(long[] u : P)if(u[0] == 0)p0 = u[1];
		assert p0 != 0;

		long ip0 = invl(p0, mod);
		Q[0] = n >= 0 ? pow(p0, n, mod) : pow(ip0, n, mod);
		for(int i = 0;i < m;i++){
			long s = 0;
			for (long[] u : P) {
				if (Math.max(0, i + 1 - P.length + 1) <= i - u[0] + 1 && i - u[0] + 1 <= i) {
					s += u[0] * u[1] % mod * Q[i - (int) u[0] + 1];
					if(s >= big)s -= big;
				}
			}
			s %= mod;
			long t = 0;
			for(long[] u : P) {
				if (Math.max(0, i - P.length + 1) <= i - u[0] && i - u[0] <= i - 1) {
					t += (i-u[0]+1) * u[1] % mod * Q[i - (int) u[0] + 1];
					if(t >= big)t -= big;
				}
			}
			t %= mod;
			s = (s*n-t) % mod;
			if(s < 0)s += mod;
			Q[i+1] = s * ip0 % mod * invl(i+1, mod) % mod;
		}
		return Q;
	}

	/**
	 * n=500000, K=10^9でpowより1.76倍遅い
	 * @param a
	 * @param K
	 * @return
	 */
	public static long[] powNaive(long[] a, int K)
	{
		int n = a.length;
		long[] ret = {1};
		for(int d = 31-Integer.numberOfLeadingZeros(K);d >= 0;d--) {
			ret = mul(ret, ret, n);
			if(K<<~d<0) {
				ret = mul(ret, a, n);
			}
		}
		return ret;
	}

	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 long invl(long a) {
		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 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)
	{
		for(int i = 0, j = p.length-1;i < j;i++,j--){
			long d = p[i]; p[i] = p[j]; p[j] = d;
		}
		return 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.
	//
	// deg(f)=n, deg(g)=m, f=gq+r, f=gq+r.
	// f* = x^n*f(1/x),
	// t=g*^-1 mod x^(n-m+1), q=(tf* mod x^(n-m+1))*
	public static long[][] div(long[] f, long[] g)
	{
		int n = f.length, m = g.length;
		if(n < m)return new long[][]{new long[0], Arrays.copyOf(f, n)};
		long[] rf = reverse(f, n-m+1);
		long[] rg = reverse(g, n-m+1);
		long[] rq = mul(rf, inv(rg), n-m+1);
		long[] q = reverse(rq, n-m+1);
		long[] r = sub(f, mul(q, g, m-1), m-1);
		return new long[][]{q, r};
	}

	public static long[] mulAll(List<long[]> sup)
	{
		PriorityQueue<long[]> ps = new PriorityQueue<>((x, y) -> x.length - y.length);
		ps.addAll(sup);
		while(ps.size() > 1)ps.add(mul(ps.poll(), ps.poll()));
		return ps.poll();
	}

	public static class NTTStockham998244353 {
		private static final int P = 998244353, mod = P, G = 3;
		private static long[] wps;

		public static long[] convolve(long[] a, long[] b)
		{
			int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);

			wps = new long[m];
			long unit = pow(G, (P-1)/m);
			wps[0] = 1;
			for(int p = 1;p < m;p++) {
				wps[p] = wps[p-1] * unit % mod;
			}

			long[] fa = go(a, m, false);
			long[] fb = a == b ? fa : go(b, m, false);
			for(int i = 0;i < m;i++){
				fa[i] = fa[i]*fb[i] % mod;
			}
			fa = go(fa, m, true);
			for(int i = 1, j = m-1;i < j;i++,j--) {
				long d = fa[i]; fa[i] = fa[j]; fa[j] = d;
			}
			return fa;
		}

		private static void fft(long[] X, long[] Y)
		{
			int s = 1;
			boolean eo = false;
			for(int n = X.length;n >= 4;n /= 2) {
				int m = n/2;
				for(int p = 0;p < m;p++) {
					long wp = wps[s*p];
					long wk = (wp<<32)/P;
					for(int q = 0;q < s;q++) {
						long a = X[q + s*(p+0)];
						long b = X[q + s*(p+m)];
						long ndsts = a + b;
						if(ndsts >= 2*P)ndsts -= 2*P;
						long T = a - b + 2*P;
						long Q = wk*T>>>32;
						Y[q + s*(2*p+0)] = ndsts;
						Y[q + s*(2*p+1)] = wp*T-Q*P&(1L<<32)-1;
					}
				}
				s *= 2;
				eo = !eo;
				long[] D = X; X = Y; Y = D;
			}
			long[] z = eo ? Y : X;
			for(int q = 0;q < s;q++) {
				long a = X[q + 0];
				long b = X[q + s];
				z[q+0] = (a+b) % P;
				z[q+s] = (a-b+2*P) % P;
			}
		}

//	private static void fft(long[] X, long[] Y)
//	{
//		int s = 1;
//		boolean eo = false;
//		for(int n = X.length;n >= 4;n /= 2) {
//			int m = n/2;
//			for(int p = 0;p < m;p++) {
//				long wp = wps[s*p];
//				for(int q = 0;q < s;q++) {
//					long a = X[q + s*(p+0)];
//					long b = X[q + s*(p+m)];
//					Y[q + s*(2*p+0)] = (a+b) % P;
//					Y[q + s*(2*p+1)] = (a-b+P) * wp % P;
//				}
//			}
//			s *= 2;
//			eo = !eo;
//			long[] D = X; X = Y; Y = D;
//		}
//		long[] z = eo ? Y : X;
//		for(int q = 0;q < s;q++) {
//			long a = X[q + 0];
//			long b = X[q + s];
//			z[q+0] = (a+b) % P;
//			z[q+s] = (a-b+P) % P;
//		}
//	}

		private static long[] go(long[] src, int n, boolean inverse)
		{
			long[] dst = Arrays.copyOf(src, n);
			fft(dst, new long[n]);
			if(inverse){
				long in = invl(n);
				for(int i = 0;i < n;i++){
					dst[i] = dst[i] * in % mod;
				}
			}

			return dst;
		}

		private static long pow(long a, long n) {
			//		a %= mod;
			long ret = 1;
			int x = 63 - Long.numberOfLeadingZeros(n);
			for (; x >= 0; x--) {
				ret = ret*ret % mod;
				if (n<<~x<0)ret = ret*a%mod;
			}
			return ret;
		}

		private static long invl(long a) {
			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 C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n) return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}


	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 void main(String[] args) {
		new No2605().run();
	}

	public void run()
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);

		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
		//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
		//			@Override
		//			public void run() {
		//				long s = System.currentTimeMillis();
		//				solve();
		//				out.flush();
		//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
		//			}
		//		};
		//		t.start();
		//		t.join();
	}

	private boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}

	private final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){
			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[][] nmi(int n, int m)
	{
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(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 long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){ return write(c).writeln(); }
		public FastWriter writeln(int x){ return write(x).writeln(); }
		public FastWriter writeln(long x){ return write(x).writeln(); }
		public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(IntUnaryOperator f, int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsInt(x));
			}
			return this;
		}

		public FastWriter write(LongUnaryOperator f, long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsLong(x));
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs) { return write(xs).writeln(); }
		public FastWriter writeln(long... xs) { return write(xs).writeln(); }
		public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(char[] line) { return write(line).writeln(); }
		public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }
		public FastWriter writeln(String s) { return write(s).writeln(); }

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }
		public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }
		public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public static void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public static void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public static void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public static void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
yukicoder

結果

テストケース

ソースコード
