Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.HashMap;
import java.util.Map;
import java.util.NoSuchElementException;

public class Main {

	public static void main(String[] args) throws IOException {
		new Main().solve();
	}

	private void solve() throws IOException {
		try {
			//			solveA();
			//			solveB();
			solveC();
			//			solveC2();
			// solveD();
			// solveE();
			// solveF();
		} finally {
			if (in != null) {
				in.close();
			}
			if (out != null) {
				out.flush();
				out.close();
			}
		}

	}

	private void solveA() {
		int numA = nextInt();
		int numB = nextInt();
		int numC = nextInt();
		int numD = nextInt();

		out.println(numA * numB > numC * numD ? numA * numB : numC * numD);

	}

	private void solveB() {
		int numN = nextInt();
		char[] strS = next().toCharArray();

		int x = 0;
		int res = 0;
		for (int i = 0; i < strS.length; i++) {
			if (strS[i] == 'I') {
				x++;
			} else if (strS[i] == 'D') {
				x--;
			}
			res = Math.max(res, x);
		}

		out.println(res);
	}

	private void solveC2() {

		long CONST = (long) Math.pow(10, 9) + 7;
		int numN = nextInt();

		BigDecimal kaijou = BigDecimal.ONE;
		for (int i = 1; i <= numN; i++) {
			kaijou = kaijou.multiply(new BigDecimal(i));
		}

		BigDecimal result = BigDecimal.ONE;
		BigDecimal index = new BigDecimal("2");
		BigDecimal lKaijou = new BigDecimal(kaijou.toString());
		while (index.compareTo(lKaijou) < 0) {

			//約数
			BigDecimal yakusu = BigDecimal.ZERO;
			while (kaijou.remainder(index).equals(BigDecimal.ZERO)) {
				yakusu = yakusu.add(BigDecimal.ONE);
				kaijou = kaijou.divide(index);
			}
			if (!yakusu.equals(BigDecimal.ZERO)) {
				yakusu = yakusu.add(BigDecimal.ONE);
				result = result.multiply(yakusu);
			}
			index = index.add(BigDecimal.ONE);
		}

		out.println(result.remainder(new BigDecimal(CONST)));
	}

	/**
	 * 1
	 *  1
	 * 2
	 *  2^1
	 * 3
	 *  3^1
	 * 4
	 *  2^2
	 * 5
	 *  5^1
	 * 6
	 *  2^1*3^1
	 *
	 *  2^4 + 3^2 + 5^1
	 *  約数の個数なので、 (4+1)*(2+1)*(1+1) =30
	 *  ex: modを求めている場合、合計のmodは各値のmodの責に等しい
	 *   (4 * 8 * 10)%3 = 2
	 *   4%3 * 8%3 * 10%3 = 1 * 2 * 1
	 *  約数の総和なら、(2^0 + 2^1 + 2^2 + 2^3)*(3^0 + 3^1 + 3^2)*(5^0 + 5^1)
	 */
	private void solveC() {
		long CONST = (long) Math.pow(10, 9) + 7;
		int numN = nextInt();

		BigDecimal res = BigDecimal.ONE;
		//全てを合算してからではオーバーフローするので、各値を素因数分解して合計とする。
		Map<Integer, Integer> wkMap = new HashMap<Integer, Integer>();
		for (int i = 2; i <= numN; i++) {
			int temp = i;
			int yakusu = 0;
			for (int j = 2; j <= i;) {
				if (temp % j == 0) {
					yakusu++;
					temp /= j;
				} else {
					if (yakusu != 0) {
						wkMap.merge(j, yakusu, (x, y) -> x + y);
					}
					j++;
					yakusu = 0;
				}
			}
		}

		//すべてを合算してから余りを求めるとオーバーフローするので
		//合計のmodは各値のmodの責に等しいを利用
		for (Integer b : wkMap.values()) {
			//			res = ((b + 1) * res) % CONST;
			res = res.multiply(new BigDecimal(b).add(BigDecimal.ONE));
		}

		out.println(res.remainder(new BigDecimal(CONST)));
	}

	private void solveD() {
		int numN = nextInt();

		out.println("");
	}

	private void solveE() {
		int numN = nextInt();

		out.println("");
	}

	private void solveF() {
		int numN = nextInt();

		out.println("");
	}

	private final PrintWriter out = new PrintWriter(System.out);
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			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 hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	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();
		}
	}
}