結果

問題 No.940 ワープ ε=ε=ε=ε=ε=│;p>д<│
ユーザー uwiuwi
提出日時 2019-12-08 05:33:22
言語 Java21
(openjdk 21)
結果
TLE  
実行時間 -
コード長 18,441 bytes
コンパイル時間 6,009 ms
コンパイル使用メモリ 87,236 KB
実行使用メモリ 297,712 KB
最終ジャッジ日時 2023-08-27 15:44:39
合計ジャッジ時間 39,480 ms
ジャッジサーバーID
(参考情報)
judge11 / judge12
このコードへのチャレンジ(β)

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 149 ms
70,876 KB
testcase_01 AC 149 ms
70,856 KB
testcase_02 AC 150 ms
70,956 KB
testcase_03 AC 257 ms
73,644 KB
testcase_04 AC 147 ms
70,908 KB
testcase_05 AC 247 ms
72,624 KB
testcase_06 AC 213 ms
74,132 KB
testcase_07 AC 213 ms
74,152 KB
testcase_08 AC 212 ms
73,780 KB
testcase_09 AC 217 ms
74,280 KB
testcase_10 AC 212 ms
74,176 KB
testcase_11 AC 211 ms
73,620 KB
testcase_12 AC 249 ms
74,428 KB
testcase_13 AC 215 ms
74,324 KB
testcase_14 AC 160 ms
71,712 KB
testcase_15 AC 617 ms
95,120 KB
testcase_16 AC 952 ms
123,028 KB
testcase_17 AC 3,007 ms
192,768 KB
testcase_18 AC 3,106 ms
223,988 KB
testcase_19 AC 3,001 ms
192,800 KB
testcase_20 AC 3,129 ms
227,772 KB
testcase_21 AC 1,687 ms
147,668 KB
testcase_22 AC 3,114 ms
226,108 KB
testcase_23 AC 1,658 ms
145,640 KB
testcase_24 AC 3,129 ms
227,376 KB
testcase_25 TLE -
testcase_26 TLE -
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 #

package adv2019;
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 D03_2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	public static int mod = 1000000007;
	static int[][] fif = enumFIF(2200005, mod);
	
	// (-1)^i (n-k+i)! / (n-k)! / i!

	void solve()
	{
		int X = ni(), Y = ni(), Z = ni();
		int n = X+Y+Z;
		if(n == 0) {
			out.println(1);
			return;
		}
		long[] F = new long[n+1];
		for(int i = 0;i <= n;i++) {
			F[i] = C(X+i-1, i-1, mod, fif) * C(Y+i-1, i-1, mod, fif) % mod *
					C(Z+i-1, i-1, mod, fif) % mod;
		}
		
		long[] A = new long[n+1];
		long[] B = new long[n+1];
		for(int i = 0;i <= n;i++) {
			A[i] = (long)(i % 2 == 0 ? 1 : mod-1) * fif[1][i] % mod;
			B[i] = fif[0][n-i];
		}
		
		long[] C = convolute(A, B, 3, mod);
		for(int i = 0;i <= n;i++) {
			C[i] = C[i] * fif[1][n-i] % mod;
		}
		
		long ans = 0;
		for(int i = 0;i <= n;i++) {
			ans += C[i] * F[n-i];
			ans %= mod;
		}
		out.println(ans);
	}
	
	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 D03_2().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)); }
}
0