結果

問題 No.368 LCM of K-products
コンテスト
ユーザー hiromi_ayase
提出日時 2016-05-28 00:05:45
言語 Java
(openjdk 23)
結果
AC  
実行時間 183 ms / 2,000 ms
コード長 5,451 bytes
コンパイル時間 2,449 ms
コンパイル使用メモリ 89,040 KB
実行使用メモリ 58,976 KB
最終ジャッジ日時 2024-09-22 14:48:41
合計ジャッジ時間 7,983 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
other AC * 35
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ソースコード

diff # 

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;

public class Main {
	private static int[] primes = sieveAtkin(1000000);

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int N = sc.nextInt();
		int K = sc.nextInt();
		long[] a = sc.nextLongList(N);

		Map<Long, List<Long>> map = new HashMap<>();
		for (long x : a) {
			for (long[] y : factorize(x)) {
				if (!map.containsKey(y[0])) {
					map.put(y[0], new ArrayList<Long>());
				}
				map.get(y[0]).add(y[1]);
			}
		}

		for (List<Long> list : map.values()) {
			Collections.sort(list, new Comparator<Long>() {
				@Override
				public int compare(Long o1, Long o2) {
					return Long.compare(o2, o1);
				}
			});
		}

		long MOD = 1000000000 + 7;
		long ret = 1;
		for (Map.Entry<Long, List<Long>> entry : map.entrySet()) {
			List<Long> list = entry.getValue();
			long x = entry.getKey();
			long total = 0;
			for (int i = 0; i < Math.min(K, list.size()); i++) {
				total += list.get(i);
			}
			ret *= powMod(x, total, MOD);
			ret %= MOD;
		}
		System.out.println(ret);
	}

	public static long powMod(long x, long k, long mod) {
		int n = 63 - Long.numberOfLeadingZeros(k);
		long answer = 1;
		for (int i = n; i >= 0; i--) {
			answer = (answer * answer) % mod;
			if (((k >> i) & 1L) == 1L) {
				answer = (answer * x) % mod;
			}
		}
		return answer;
	}

	public static long[][] factorize(long n) {
		int rp = (int) Math.sqrt(n);
		long[][] factors = new long[100][2];
		int idx = 0;
		for (int i = 0; primes[i] <= rp; i++) {
			int p = primes[i];
			int count = 0;
			while (n % p == 0) {
				count++;
				n /= p;
			}
			if (count > 0) {
				factors[idx][0] = p;
				factors[idx][1] = count;
				idx++;
			}
			if (n == 1) {
				break;
			}
		}
		if (n != 1) {
			factors[idx][0] = n;
			factors[idx][1] = 1;
			idx++;
		}

		return Arrays.copyOf(factors, idx);
	}

	public static int[] sieveAtkin(int size) {
		boolean[] isPrime = new boolean[size + 1];
		int sqrtN = (int) Math.sqrt(size);
		int n;
		for (int x = 1; x <= sqrtN; ++x) {
			for (int y = 1; y <= sqrtN; ++y) {
				n = 4 * x * x + y * y;
				if (n <= size && (n % 12 == 1 || n % 12 == 5)) {
					isPrime[n] = !isPrime[n];
				}
				n = 3 * x * x + y * y;
				if (n <= size && n % 12 == 7) {
					isPrime[n] = !isPrime[n];
				}
				n = 3 * x * x - y * y;
				if (x > y && n <= size && n % 12 == 11) {
					isPrime[n] = !isPrime[n];
				}
			}
		}

		for (n = 5; n <= sqrtN; ++n) {
			if (isPrime[n]) {
				for (int k = n * n; k <= size; k += n * n) {
					isPrime[k] = false;
				}
			}
		}
		isPrime[2] = isPrime[3] = true;

		int[] ret = new int[size];
		int count = 0;
		for (int i = 1; i < size; i++) {
			if (isPrime[i]) {
				ret[count++] = i;
			}
		}
		return Arrays.copyOf(ret, count);
	}
}

class FastScanner {
	public static String debug = null;

	private final InputStream in = System.in;
	private int ptr = 0;
	private int buflen = 0;
	private byte[] buffer = new byte[1024];
	private boolean eos = false;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				if (debug != null) {
					buflen = debug.length();
					buffer = debug.getBytes();
					debug = "";
					eos = true;
				} else {
					buflen = in.read(buffer);
				}
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen < 0) {
				eos = true;
				return false;
			} else if (buflen == 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean isEOS() {
		return this.eos;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		return (int) nextLong();
	}

	public long[] nextLongList(int n) {
		return nextLongTable(1, n)[0];
	}

	public int[] nextIntList(int n) {
		return nextIntTable(1, n)[0];
	}

	public long[][] nextLongTable(int n, int m) {
		long[][] ret = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				ret[i][j] = nextLong();
			}
		}
		return ret;
	}

	public int[][] nextIntTable(int n, int m) {
		int[][] ret = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				ret[i][j] = nextInt();
			}
		}
		return ret;
	}
}
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