結果

問題 No.3038 フィボナッチ数列の周期
ユーザー uwiuwi
提出日時 2018-04-03 01:47:38
言語 Java21
(openjdk 21)
結果
AC  
実行時間 313 ms / 3,000 ms
コード長 6,937 bytes
コンパイル時間 6,730 ms
コンパイル使用メモリ 82,952 KB
実行使用メモリ 174,284 KB
最終ジャッジ日時 2023-09-08 13:54:11
合計ジャッジ時間 13,285 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
このコードへのチャレンジ
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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 284 ms
173,764 KB
testcase_01 AC 286 ms
173,876 KB
testcase_02 AC 287 ms
173,908 KB
testcase_03 AC 289 ms
173,884 KB
testcase_04 AC 292 ms
173,932 KB
testcase_05 AC 289 ms
174,036 KB
testcase_06 AC 290 ms
173,768 KB
testcase_07 AC 289 ms
173,844 KB
testcase_08 AC 294 ms
173,760 KB
testcase_09 AC 289 ms
173,928 KB
testcase_10 AC 298 ms
173,840 KB
testcase_11 AC 296 ms
174,272 KB
testcase_12 AC 291 ms
173,932 KB
testcase_13 AC 289 ms
173,868 KB
testcase_14 AC 289 ms
173,860 KB
testcase_15 AC 291 ms
173,928 KB
testcase_16 AC 306 ms
173,848 KB
testcase_17 AC 307 ms
174,284 KB
testcase_18 AC 313 ms
173,956 KB
testcase_19 AC 309 ms
173,904 KB
testcase_20 AC 311 ms
173,848 KB
testcase_21 AC 311 ms
173,924 KB
testcase_22 AC 305 ms
174,032 KB
testcase_23 AC 306 ms
173,812 KB
testcase_24 AC 309 ms
173,768 KB
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ソースコード

diff # 

package af2018;
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 N3038 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] lpf = enumLowestPrimeFactors(20000003);
//		int[] primes = sieveEratosthenes(10000005);
		int[] es = new int[10000006];
		
		int[] ps = new int[n];
		int[] ks = new int[n];
		for(int i = 0;i < n;i++){
			ps[i] = ni();
			ks[i] = ni();
			if(ps[i] != 5){
				int P = pisano(ps[i], lpf);
				int[][] f = factorFast(P, lpf);
				
				es[ps[i]] = Math.max(es[ps[i]], ks[i]-1);
				for(int[] u : f){
					es[u[0]] = Math.max(es[u[0]], u[1]);
				}
			}else{
				es[5] = Math.max(es[5], ks[i]);
				es[2] = Math.max(es[2], 2);
			}
			
			// P*p^(k-1)
		}
		
		long ans = 1;
		for(int i = 0;i < es.length;i++){
			if(es[i] > 0){
				ans = ans * pow(i, es[i], 1000000007) % 1000000007;
			}
		}
		out.println(ans);
		
//		for(int p : primes){
//			tr(p, pisano(p, lpf));
//		}
	}
	
	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 int[][] factorFast(int n, int[] lpf)
	{
		int[][] f = new int[9][];
		int q = 0;
		while(lpf[n] > 0){
			int p = lpf[n];
			if(q == 0 || p != f[q-1][0]){
				f[q++] = new int[]{p, 1};
			}else{
				f[q-1][1]++;
			}
			n /= p;
		}
		if(n > 1){
			// big prime
			return new int[][]{{n, 1}};
		}
		return Arrays.copyOf(f, q);
	}

	
	
	public static int[] enumLowestPrimeFactors(int n) {
		int tot = 0;
		int[] lpf = new int[n + 1];
		int u = n + 32;
		double lu = Math.log(u);
		int[] primes = new int[(int) (u / lu + u / lu / lu * 1.5)];
		for (int i = 2; i <= n; i++)
			lpf[i] = i;
		for (int p = 2; p <= n; p++) {
			if (lpf[p] == p)
				primes[tot++] = p;
			int tmp;
			for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) {
				lpf[tmp] = primes[i];
			}
		}
		return lpf;
	}

	
	int pisano(int p, int[] lpf)
	{
		if(p == 2)return 3;
		if(p == 5)return 20;
		int b = p % 5 == 1 || p % 5 == 4 ? p - 1 : 2 * p + 2;
		for(int x = b;x > 1;x /= lpf[x]){
			if(fib(b/lpf[x], p))b /= lpf[x];
		}
		return b;
	}
	
	public static boolean fib(long n, long mod)
	{
		long a = 1, b = 1, d = 0;
		long va = 1, vb = 0;
		
		// (1 1)(1)
		// (1 0)(0)
		for(;n>0;n>>>=1){
			if((n&1)==1){
				long nva = (a*va+b*vb)%mod;
				long nvb = (b*va+d*vb)%mod;
				va = nva; vb = nvb;
			}
			
			long na = (a*a+b*b)%mod;
			long nb = (b*(a+d))%mod;
			long nd = (d*d+b*b)%mod;
			a = na; b = nb; d = nd;
		}
		
		return va == 1 && vb == 0;
	}

	
	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);
	}

	
	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 N3038().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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