結果

問題 No.2181 LRM Question 2
ユーザー uwiuwi
提出日時 2023-01-06 23:52:43
言語 Java21
(openjdk 21)
結果
WA  
実行時間 -
コード長 22,494 bytes
コンパイル時間 4,472 ms
コンパイル使用メモリ 94,184 KB
実行使用メモリ 57,368 KB
最終ジャッジ日時 2024-11-30 20:56:20
合計ジャッジ時間 10,356 ms
ジャッジサーバーID
(参考情報)
judge5 / judge2
このコードへのチャレンジ
(要ログイン)

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 63 ms
37,928 KB
testcase_01 AC 63 ms
38,092 KB
testcase_02 WA -
testcase_03 AC 63 ms
38,064 KB
testcase_04 AC 65 ms
38,044 KB
testcase_05 AC 62 ms
38,100 KB
testcase_06 AC 60 ms
38,028 KB
testcase_07 AC 60 ms
37,568 KB
testcase_08 AC 321 ms
40,484 KB
testcase_09 WA -
testcase_10 AC 441 ms
40,412 KB
testcase_11 AC 674 ms
40,480 KB
testcase_12 AC 583 ms
40,484 KB
testcase_13 AC 64 ms
37,808 KB
testcase_14 AC 115 ms
45,776 KB
testcase_15 AC 71 ms
38,020 KB
testcase_16 AC 118 ms
43,808 KB
testcase_17 AC 77 ms
37,832 KB
testcase_18 AC 69 ms
38,192 KB
testcase_19 AC 67 ms
38,064 KB
testcase_20 AC 90 ms
40,516 KB
testcase_21 AC 132 ms
39,224 KB
testcase_22 AC 67 ms
38,160 KB
testcase_23 AC 60 ms
37,744 KB
testcase_24 AC 64 ms
38,008 KB
testcase_25 AC 72 ms
38,136 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 #

package contest230106;

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

public class G2 {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	public void solve()
	{
		cache.clear();
		cache2.size = 0;
		long L = nl(), R = nl();
		int mod = ni();
		// i < mod and n-(i+1) < modのときだけ非0
		// i+1 > n-mod
		// n-mod-1 < i < mod
		// n-mod < mod
		// n < 2*mod

		// n^2*(n-1)^2*..*(n-i+1)^2 * (i+1)^2*...*n^2
		// -------------------------------------------
		// 1^2*2^2*...n^2

		// n^2*(n-1)^2*..*(n-i+1)^2
		// -------------------------------------------
		// 1^2*2^2*...i^2

		// C(n,i)^2

		// sum_n sum_{i=1}^{n-1} C(n,i)^2 = (2n)!/(n!)^2-2
		// (2n)(2n-1)(2n-2)...(n+1)
		// -------------------------
		// n..........1

		int[] primes = sieveEratosthenes(1000);
		int[][] F = factor(mod, primes);

		long ans = -2*(R-L+1);
		long gmod = 1;
		long gval = 0;
		for(int[] item : F){
			fif = enumFIF(item[0]-1, item[0]);
			long mo = 1;
			for(int j = 0;j < item[1];j++){
				mo = mo * item[0];
			}
			long s = 0;
			for(int i = 0;i < R-L+1;i++){
				long n = L+i;
				long val = C(2*n, n, item[0], item[1]);
				s += val;
			}
			s %= mo;
			gval = crt(gmod, gval, mo, s);
			gmod *= mo;
		}
		ans += gval;
		ans %= mod;
		if(ans < 0)ans += mod;
		out.println(ans);
	}

	static int[][] fif;

	public static int[][] factor(int n, int[] primes)
	{
		int[][] ret = new int[9][2];
		int rp = 0;
		for(int p : primes){
			if(p * p > n)break;
			int i;
			for(i = 0;n % p == 0;n /= p, i++);
			if(i > 0){
				ret[rp][0] = p;
				ret[rp][1] = i;
				rp++;
			}
		}
		if(n != 1){
			ret[rp][0] = n;
			ret[rp][1] = 1;
			rp++;
		}
		return Arrays.copyOf(ret, rp);
	}


	public static long crt(long p, long m, long q, long n)
	{
		assert p > 0;
		assert q > 0;
		assert 0 <= m;
		assert m < p;
		assert 0 <= n;
		assert n < q;
		if(p < q)return crt(q, n, p, m);

		long a = p, b = q;
		long pp = 1, qq = 0;
		while(b > 0){
			long c = a / b;
			long d;
			d = a; a = b; b = d % b;
			d = pp; pp = qq; qq = d - c * qq;
		}
		if((n - m) % a != 0)return -1;
		long mod = p / a * q;
//		long ret = (p * pp % mod * ((n - m) / a) + m) % mod;
		long ret = ((n-m)*pp%q) * (p/a) + m;
		if(ret < 0)ret += mod;
		return ret;
	}

	public static int[] sieveEratosthenes(int n) {
		if (n <= 32) {
			int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
			for (int i = 0; i < primes.length; i++) {
				if (n < primes[i]) {
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isnp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
		for (int tp : tprimes) {
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31);
			for (int j = 0; j < sup; j += tp) {
				for (int i = 0; i < tp && i + j < sup; i++) {
					isnp[j + i] |= ptn[i];
				}
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14};
		int h = n / 2;
		for (int i = 0; i < sup; i++) {
			for (int j = ~isnp[i]; j != 0; j &= j - 1) {
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if (p > n) break;
				ret[pos++] = p;
				if ((long) p * p > n) continue;
				for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q;
			}
		}

		return Arrays.copyOf(ret, pos);
	}

	static Map<Integer, long[][]> cache = new HashMap<>();

	public static long CY(long n, long r, int p, int[][] fif)
	{
		if(r < 0 || r > n)return 0;

		long ret = 1;
		for(;n > 0; n /= p, r /= p){
			int np = (int)(n%p), rp = (int)(r%p);
			if(np < rp)return 0;
			int nrp = np-rp;
			if(nrp < 0)nrp += p;
			ret = ret*fif[0][np]%p*fif[1][rp]%p*fif[1][nrp]%p;
		}
		return ret;
	}


	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 C(long n, long r, int p, int q)
	{
		if(q == 1){
			return CY(n, r, p, fif);
		}
		if(r < 0 || r > n)return 0;
		long P = 1;
		for(int i = 0;i < q;i++)P *= p;

		long z = n - r;
		long e0 = 0;
		for(long u = n/p;u > 0;u /= p)e0 += u;
		for(long u = r/p;u > 0;u /= p)e0 -= u;
		for(long u = z/p;u > 0;u /= p)e0 -= u;
		if(e0 >= q)return 0;

//		long em = 0;
//		for(long u = n/P*p;u > 0;u /= p)em += u;
//		for(long u = r/P*p;u > 0;u /= p)em -= u;
//		for(long u = z/P*p;u > 0;u /= p)em -= u;

		if(!cache.containsKey(p)){
			long[] fact = new long[p*(q+1)+1];
			long[] ifact = new long[p*(q+1)+1];
			fact[0] = ifact[0] = 1;
			for(int i = 1;i <= p*(q+1);i++){
				if(i % p == 0){
					fact[i] = fact[i-1];
				}else{
					fact[i] = mul(fact[i-1], i, P);
				}
				ifact[i] = invl(fact[i], P);
			}
			cache.put(p, new long[][]{fact, ifact});
		}

		long[] fact = cache.get(p)[0];
		long[] ifact = cache.get(p)[1];

		long num = 1;
		long den = 1;
		while(n > 0){
			num = num * ff(n, p, (int)(q-e0), fact, ifact) % P;
			den = den * ff(r, p, (int)(q-e0), fact, ifact) * ff(z, p, (int)(q-e0), fact, ifact) % P;
			n /= p; r /= p; z /= p;
		}
		long ret = num * invl(den, P) * pow(p, e0, P) % P;
//			if(!(p == 2 && q >= 3) && (em&1)==1){
//				tr("kimasi");
//				ret = (P-ret) % P;
//			}

		return ret;
	}

	public static class LongHashMapWithoutDeletion {
		int[] first;
		int[] next;
		long[] keys;
		int[] vals;
		int size;
		int scale;

		public LongHashMapWithoutDeletion() {
			scale = 1;
			keys = new long[1 << scale];
			vals = new int[1 << scale];
			first = new int[1 << scale];
			next = new int[1 << scale];
			size = 0;
			Arrays.fill(first, -1);
			Arrays.fill(next, -1);
		}

		public void rehash() {
			scale++;
			keys = Arrays.copyOf(keys, 1 << scale);
			vals = Arrays.copyOf(vals, 1 << scale);
			first = new int[1 << scale];
			next = new int[1 << scale];
			Arrays.fill(first, -1);
			Arrays.fill(next, -1);
			for (int i = 0; i < 1 << scale - 1; i++) {
				int h = h(keys[i]) & (1 << scale) - 1;
				next[i] = first[h];
				first[h] = i;
			}
		}

		public void put(long key, int val) {
			int h = h(key) & (1 << scale) - 1;
			int ind = search(h, key);
			if (ind >= keys.length) {
				rehash();
				h = h(key) & (1 << scale) - 1;
			}
			if (ind < size) {
				vals[ind] = val;
			} else {
				keys[ind] = key;
				vals[ind] = val;
				next[ind] = first[h];
				first[h] = ind;
				size++;
			}
		}

		public boolean containsKey(long key) {
			int h = h(key) & (1 << scale) - 1;
			int ind = search(h, key);
			return ind < size;
		}

		public int get(long key) {
			int h = h(key) & (1 << scale) - 1;
			int ind = search(h, key);
			return ind >= size ? 0 : vals[ind];
		}

		private int search(int h, long key) {
			for (int f = first[h]; f != -1; f = next[f]) {
				if (keys[f] == key) return f;
			}
			return size;
		}

		private int h(long x) {
			x ^= x >>> 33;
			x *= 0xff51afd7ed558ccdL;
			x ^= x >>> 33;
			x *= 0xc4ceb9fe1a85ec53L;
			x ^= x >>> 33;
			return (int) (x ^ x >>> 32);
		}
	}


	static LongHashMapWithoutDeletion cache2 = new LongHashMapWithoutDeletion();

	public static long ff(long n, int p, int q, long[] fact, long[] ifact)
	{
		long code = n;
		code = code*1000000009 + p;
		code = code*1000000009 + q;
		if(cache2.containsKey(code))return cache2.get(code);

		long u = n/p;
		int v = (int)(n%p);
		boolean plused = q % 2 == 0;
		if(plused)q++;

		int r = (q-1)/2;
		long P = 1;
		for(int j = 1;j <= q;j++)P *= p;
		long PP = P / p * (p-1);
//		tr(n, p, q, u, v, r, P, PP);

		long ret = fact[v];
		outer:
		for(int j = 1;j <= r;j++){
			long[] betanums = new long[2*r+1];
			long sign = 1;
			for(int i = -r;i <= r;i++){
				if(i != j && -i != j){
					if(u-i == 0)continue outer;
					betanums[i+r] = u-i;
					if(betanums[i+r] < 0){
						sign *= -1;
						betanums[i+r] *= -1;
					}
				}
			}
			for(int i = -r;i <= r;i++){
				if(i != j && -i != j){
					long w = j-i;
					if(w < 0){
						sign *= -1;
						w *= -1;
					}
					for(int k = 0;k <= 2*r;k++){
						if(betanums[k] != 0){
							long g = gcd(betanums[k], w);
							betanums[k] /= g;
							w /= g;
						}
					}
					if(w != 1){
//						throw new AssertionError("dead");
					}
				}
			}
			long beta = sign == -1 ? PP-1 : 1;
			for(int k = 0;k <= 2*r;k++){
				if(betanums[k] > 0){
					beta = mul(beta, betanums[k], PP);
				}
			}

			long po = pow(fact[j*p], beta, P);
			ret = mul(ret, po, P);
		}
		if(p == 2 && ((u*2%8 >= 3 && u*2%8 < 7) != (ret % 4 == 3)))ret = P-ret;

		outer2:
		for(int j = 1;j <= q-1;j++){
			long cell = fact[j*p+v] * ifact[j*p] * ifact[v] % P;
			long[] alphanums = new long[q];
			long sign = 1;
			for(int i = 0;i <= q-1;i++){
				if(i != j){
					alphanums[i] = u-i;
					if(u-i == 0)continue outer2;
					if(alphanums[i] < 0){
						sign *= -1;
						alphanums[i] *= -1;
					}
				}
			}
			for(int i = 0;i <= q-1;i++){
				if(i != j){
					long w = j-i;
					if(w < 0){
						sign *= -1;
						w *= -1;
					}
					for(int k = 0;k <= q-1;k++){
						if(alphanums[k] != 0){
							long g = gcd(alphanums[k], w);
							alphanums[k] /= g;
							w /= g;
						}
					}
					if(w != 1){
//						throw new AssertionError("dead2");
					}
				}
			}
			long alpha = sign == -1 ? PP-1 : 1;
			for(int k = 0;k <= q-1;k++){
				if(alphanums[k] > 0){
					alpha = alpha * (alphanums[k] % PP) % PP;
				}
			}
//			tr("alpha", j, r, cell, alpha);
//			System.err.println(alpha + " " + P + " " + PP);
			ret = ret * pow(cell, alpha, P) % P;
		}

		if(plused){
			cache2.put(code, (int)(ret % (P/p)));
			return ret % (P/p);
		}else{
			cache2.put(code, (int)ret);
			return ret;
		}
	}

	public static long gcd(long a, long b) {
		while (b > 0) {
			long c = a;
			a = b;
			b = c % b;
		}
		return a;
	}


	public static long mul(long a, long b, long mod)
	{
		return a*b%mod;
//		if(a >= mod || a < 0)a %= mod;
//		if(a < 0)a += mod;
//		if(b >= mod || b < 0)b %= mod;
//		if(b < 0)b += mod;
//
//		long ret = 0;
//		int x = 63-Long.numberOfLeadingZeros(b);
//		for(;x >= 0;x--){
//			ret += ret;
//			if(ret >= mod)ret -= mod;
//			if(b<<~x<0){
//				ret += a;
//				if(ret >= mod)ret -= mod;
//			}
//		}
//		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 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 void main(String[] args) {
		new G2().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)); }
}
0