結果

問題 No.963 門松列列（2）
ユーザー 37zigen37zigen
提出日時 2019-12-12 22:55:57
言語 Java21
(openjdk 21)
結果
AC  
実行時間 1,685 ms / 3,000 ms
コード長 19,282 bytes
コンパイル時間 2,924 ms
コンパイル使用メモリ 93,816 KB
実行使用メモリ 106,764 KB
最終ジャッジ日時 2024-06-25 20:46:27
合計ジャッジ時間 12,067 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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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 159 ms
55,984 KB
testcase_01 AC 157 ms
56,416 KB
testcase_02 AC 160 ms
56,340 KB
testcase_03 AC 160 ms
56,052 KB
testcase_04 AC 159 ms
56,232 KB
testcase_05 AC 1,058 ms
86,204 KB
testcase_06 AC 449 ms
67,204 KB
testcase_07 AC 1,039 ms
85,392 KB
testcase_08 AC 1,678 ms
101,800 KB
testcase_09 AC 1,685 ms
103,560 KB
testcase_10 AC 1,684 ms
106,764 KB
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

diff # 

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 Main {
	InputStream is;
	PrintWriter out;
	String INPUT = "";

	public static int mod = 1012924417;
	static int[][] fif = enumFIF(2200005, mod);

	void solve() {
		int N = ni();
		long[] cos0 = new long[N / 2 + 5];
		long[] sin0 = new long[N / 2 + 5];
		for (int i = 0; i < cos0.length; i++) {
			cos0[i] = (long) fif[1][2 * i] * (i % 2 == 0 ? 1 : mod - 1) % mod;
		}
		for (int i = 0; i < sin0.length; i++) {
			sin0[i] = (long) fif[1][2 * i + 1] * (i % 2 == 0 ? 1 : mod - 1) % mod;
		}
		cos0 = inv(cos0);
		sin0 = convolute(sin0, cos0, 3, mod);
		long[] ret = new long[N + 1];
		for (int i = 0; i < sin0.length && 2 * i + 1 < ret.length; ++i) {
			ret[2 * i + 1] = sin0[i];
		}
		for (int i = 0; i < cos0.length && 2 * i < ret.length; ++i) {
			ret[2 * i] += cos0[i];
			ret[2 * i] %= mod;
		}
		out.println(2 * ret[N] * fif[0][N] % mod);
	}

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

	// 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);
	}
//	
//	// 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);
	}

	// 1/(1-F)-1
	static long[] transformInvertly(long[] a) {
		long[] b = new long[a.length];
		for (int i = 0; i < a.length; i++) {
			b[i] = mod - a[i];
			if (b[i] == mod)
				b[i] = 0;
		}
		if (++b[0] == mod)
			b[0] = 0;
		long[] ret = inv(b);
		if (--ret[0] < 0)
			ret[0] += mod;
		return ret;
	}

	// -1/(1+F)+1
	static long[] transformInverseOfInvertly(long[] a) {
		long[] b = new long[a.length];
		for (int i = 0; i < a.length; i++) {
			b[i] = a[i];
		}
		if (++b[0] == mod)
			b[0] = 0;
		long[] ret = inv(b);
		for (int i = 0; i < a.length; i++) {
			ret[i] = mod - ret[i];
			if (ret[i] == mod)
				ret[i] = 0;
		}
		if (++ret[0] == mod)
			ret[0] = 0;
		return ret;
	}

	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 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;
	}

	// Modified Shoup + Barrett
	private static long[] nttsb(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;

		long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
		long[] wws = new long[1 << h - 1];
		long[] ws = new long[1 << h - 1];
		long w = 1;
		for (int k = 0; k < 1 << h - 1; k++) {
			wws[k] = (w << 32) / P;
			ws[k] = w;
			w = modh(w * dw, M, H, P);
		}
		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 ndsts = dst[s] + dst[t];
					if (ndsts >= 2 * P)
						ndsts -= 2 * P;
					long T = dst[s] - dst[t] + 2 * P;
					long Q = wws[k] * T >>> 32;
					dst[s] = ndsts;
					dst[t] = ws[k] * T - Q * P & (1L << 32) - 1;
				}
			}
//			dw = dw * dw % P;
			if (i < h - 1) {
				for (int k = 0; k < 1 << h - i - 2; k++) {
					wws[k] = wws[k * 2];
					ws[k] = ws[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;
	}

	private 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;
	}

	private 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 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 };
	}

	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");
//		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();
	}

	public static void main(String[] args) throws Exception {
		new Main().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 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 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 ni() {
		return (int) nl();
	}

	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));
	}
}
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