結果

問題 No.613 Solitude by the window
ユーザー uwiuwi
提出日時 2017-12-11 22:42:09
言語 Java
(openjdk 23)
結果
AC  
実行時間 61 ms / 2,000 ms
コード長 5,614 bytes
コンパイル時間 4,176 ms
コンパイル使用メモリ 85,580 KB
実行使用メモリ 50,744 KB
最終ジャッジ日時 2024-12-14 06:10:35
合計ジャッジ時間 6,413 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 21
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 adv2017;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;

public class N613_2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		// (2+√3)^(2^n)
		long n = nl();
		int mod = ni();
		if(!(1 <= n && n <= 1000000000000000000L))throw new AssertionError("1<=n<=10^18");
		if(!(2 <= mod && mod <= 1100000000L))throw new AssertionError("2<=m<=1100000000");
		if(!(BigInteger.valueOf(mod).isProbablePrime(30)))throw new AssertionError("m should be prime");
		
//		int[][] M = {
//				{2, 1},
//				{3, 2}
//		};
//		int[] v = {1, 0};
//		for(int u = 1;;u++){
//			v = mul(M, v, mod);
//			if(v[0] == 1 && v[1] == 0){
//				tr(u);
//				break;
//			}
//		}
		
		if(mod <= 3){
			out.println(0);
		}else if(n >= 30){
			int[][] M = {
					{2, 1},
					{3, 2}
			};
			int[] v = {1, 0};
			int[] w = pow(M, v, pow(2, n, (long)mod*mod-1)+(long)mod*mod-1, mod);
			out.println(((long)w[0]*2+mod-2)%mod);
		}else{
			int[][] M = {
					{2, 1},
					{3, 2}
			};
			int[] v = {1, 0};
			int[] w = pow(M, v, 1L<<n, mod);
			out.println((w[0]*2+mod-2)%mod);
		}
	}
	
	public static long mulRobust(long a, long b, long 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 step = Long.numberOfLeadingZeros(mod)-1;
		for(int x = 63-Long.numberOfLeadingZeros(b);x >= 0;x-=step){
			int shift = Math.min(x+1, step);
			ret<<=shift;
			ret %= mod;
			
			ret += a*(b>>>x-shift+1&(1L<<shift)-1);
			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 = mulRobust(ret, ret, mod);
			if (n << 63 - x < 0)
				ret = mulRobust(ret, a, mod);
		}
		return ret;
	}

	
	// A^e*v
	public static int[] pow(int[][] A, int[] v, long e, int mod)
	{
		int[][] MUL = A;
		for(int i = 0;i < v.length;i++)v[i] %= mod;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v, mod);
			MUL = p2(MUL, mod);
		}
		return v;
	}
	
	
	// int matrix * int vector
	public static int[] mul(int[][] A, int[] v, int mod)
	{
		int m = A.length;
		int n = v.length;
		int[] w = new int[m];
		for(int i = 0;i < m;i++){
			long sum = 0;
			for(int k = 0;k < n;k++){
				sum += (long)A[i][k] * v[k];
				sum %= mod;
			}
			w[i] = (int)sum;
		}
		return w;
	}
	
	// int matrix^2 (cannot ensure negative values)
	public static int[][] p2(int[][] A, int mod)
	{
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				long sum = 0;
				for(int k = 0;k < n;k++){
					sum += (long)A[i][k] * A[k][j];
					sum %= mod;
				}
				C[i][j] = (int)sum;
			}
		}
		return C;
	}

	
	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 N613_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)); }
}
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