結果

問題 No.2181 LRM Question 2
ユーザー uwiuwi
提出日時 2023-01-07 01:22:29
言語 Java21
(openjdk 21)
結果
AC  
実行時間 1,390 ms / 2,000 ms
コード長 18,590 bytes
コンパイル時間 4,361 ms
コンパイル使用メモリ 97,892 KB
実行使用メモリ 45,324 KB
最終ジャッジ日時 2024-11-30 22:17:03
合計ジャッジ時間 13,075 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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 70 ms
37,740 KB
testcase_01 AC 66 ms
37,952 KB
testcase_02 AC 751 ms
42,928 KB
testcase_03 AC 62 ms
37,732 KB
testcase_04 AC 67 ms
37,784 KB
testcase_05 AC 64 ms
37,424 KB
testcase_06 AC 69 ms
37,556 KB
testcase_07 AC 60 ms
37,780 KB
testcase_08 AC 987 ms
43,112 KB
testcase_09 AC 406 ms
43,300 KB
testcase_10 AC 1,285 ms
42,868 KB
testcase_11 AC 1,390 ms
43,200 KB
testcase_12 AC 1,378 ms
43,248 KB
testcase_13 AC 77 ms
37,748 KB
testcase_14 AC 97 ms
45,324 KB
testcase_15 AC 68 ms
37,996 KB
testcase_16 AC 124 ms
45,320 KB
testcase_17 AC 115 ms
39,164 KB
testcase_18 AC 89 ms
38,720 KB
testcase_19 AC 78 ms
37,488 KB
testcase_20 AC 86 ms
39,548 KB
testcase_21 AC 202 ms
40,516 KB
testcase_22 AC 94 ms
39,216 KB
testcase_23 AC 65 ms
37,760 KB
testcase_24 AC 66 ms
37,288 KB
testcase_25 AC 64 ms
37,428 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.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class G5 {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	public void solve()
	{
		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

		CombinationGeneralMultipleSmall cgm = new CombinationGeneralMultipleSmall(mod);

		long ans = -2*(R-L+1);
		long s = 0;
		for(int i = 0;i < R-L+1;i++){
			long n = L+i;
//			long val = cgm.C(2*n, n);
			long val = cgm.Center(n);
			s += val;
		}
		ans += s;
		ans %= mod;
		if(ans < 0)ans += mod;
		out.println(ans);
	}

	public static class CombinationGeneralMultipleSmall {

		int[][] f;
		long[][] pesmap;
		int[] qmap;
		long[][] aprs;

		public CombinationGeneralMultipleSmall(int mod)
		{
			int[] primes = sieveEratosthenes((int)Math.sqrt(mod));
			f = factor(mod, primes);
			pesmap = new long[f.length][];
			qmap = new int[f.length];
			for(int j = 0;j < f.length;j++){
				int[] u = f[j];
				int P = u[0], e = u[1];
				int Q = (int)Math.pow(P, e);
				long[] pes = new long[Q];
				pes[0] = 1;
				for(int i = 1;i < Q;i++){
					if(i % P == 0){
						pes[i] = pes[i-1];
					}else{
						pes[i] = pes[i-1] * i % Q;
					}
				}
				pesmap[j] = pes;
				qmap[j] = Q;
			}
			aprs = aprs(qmap);
		}

		public long C(long n, long m)
		{
			if(m < 0 || m > n)return 0L;
			long[] mods = new long[f.length];
			for(int i = 0;i < f.length;i++){
				mods[i] = C(n, m, i);
			}

			return crt(qmap, mods, aprs);
		}

		private long C(long n, long m, int pind)
		{
			if(m < 0 || m > n)return 0L;
			int P = f[pind][0], e = f[pind][1];
			long pe = 0;
			int mod = qmap[pind];
			long num = 1;
			long den = 1;
			for(long x = n;x > 0;x /= P){
				num = num * F(x, pind) % mod;
				pe += x/P;
			}
			for(long x = m;x > 0;x /= P){
				den = den * F(x, pind) % mod;
				pe -= x/P;
			}
			for(long x = n-m;x > 0;x /= P){
				den = den * F(x, pind) % mod;
				pe -= x/P;
			}
			if(pe >= e)return 0L;
			num = num * invl(den, mod) % mod;
			for(int i = 0;i < pe;i++){
				num = num * P % mod;
			}
//			System.err.println(Arrays.toString(new long[]{n, m, P, e, num}));
			return num;
		}

		public long Center(long n)
		{
			long[] mods = new long[f.length];
			for(int i = 0;i < f.length;i++){
				mods[i] = Center(n, i);
			}

			return crt(qmap, mods, aprs);
		}

		private long Center(long n, int pind)
		{
			int P = f[pind][0], e = f[pind][1];
			long pe = 0;
			int mod = qmap[pind];
			long num = 1;
			long den = 1;
			for(long x = 2*n;x > 0;x /= P){
				num = num * F(x, pind) % mod;
				pe += x/P;
			}
			long minus = 0;
			for(long x = n;x > 0;x /= P){
				den = den * F(x, pind) % mod;
				minus += x/P;
			}
			pe -= 2*minus;
			den = den * den % mod;
			if(pe >= e)return 0L;
			num = num * invl(den, mod) % mod;
			for(int i = 0;i < pe;i++){
				num = num * P % mod;
			}
			return num;
		}

		public static long[][] aprs(int[] divs)
		{
			if(divs.length == 0)return null;
			long div = divs[0];
			long[][] ret = new long[divs.length][];
			for(int i = 1;i < divs.length;i++){
				ret[i] = exgcd(div, divs[i]);
				div = div * divs[i];
			}
			return ret;
		}

		public static long crt(final int[] divs, final long[] mods, long[][] aprs)
		{
			if(divs.length == 0)return 0L;
			long div = divs[0];
			long mod = mods[0];
			for(int i = 1;i < divs.length;i++){
				long[] apr = aprs[i];
				long ndiv = div * divs[i];
				mod += ((mods[i]-mod)*apr[1]%divs[i]) * div;
				div = ndiv;
			}
			mod %= div;
			if(mod < 0)mod += div;
			return mod;
		}

		public static long[] exgcd(long a, long b)
		{
			if(a == 0 || b == 0)return null;
			int as = Long.signum(a);
			int bs = Long.signum(b);
			a = Math.abs(a); b = Math.abs(b);
			long p = 1, q = 0, r = 0, s = 1;
			while(b > 0){
				long c = a / b;
				long d;
				d = a; a = b; b = d % b;
				d = p; p = q; q = d - c * q;
				d = r; r = s; s = d - c * s;
			}
			return new long[]{a, p * as, r * bs};
		}


		public long FNaive(int n, int P, int e)
		{
			long mod = 1;
			for(int i = 0;i < e;i++)mod = mod * P;

			long ret = 1;
			for(int i = 1;i <= n;i++){
				if(i % P == 0)continue;
				ret = ret * i % mod;
			}
			return ret;
		}

		public long F(long n, int pind)
		{
			int mod = qmap[pind];
			long[] pes = pesmap[pind];
			assert pes[mod-1] == 1 || pes[mod-1] == mod-1;
			long ret = pes[(int)(n%mod)];
			if(pes[mod-1] == mod-1 && n/mod%2 == 1){
				ret = mod-ret;
				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 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 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);
		}

	}


	public static void main(String[] args) {
		new G5().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