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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.lang.reflect.Field;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.TreeSet;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;


public class Main {
    public static void main(String[] args) throws Exception {
        Field f = System.out.getClass().getDeclaredField("autoFlush");
        f.setAccessible(true);
        f.set(System.out, false);
        execute(System.in, System.out);
    }

    public static void execute(InputStream in, OutputStream out) {
        ExtendedScanner s = new ExtendedScanner(in);
        Out o = new Out(out);
        solve(s, o);
        o.flush();
        o.close();
    }

    public static void solve(ExtendedScanner sc, Out out) {
        int n = sc.nextInt();
        var primes = MathUtil.eratosthenes(n);
        HashMap<Integer, Integer> fac = new HashMap<>();
        for (int i = 2; i <= n; i++) {
            int v = i;
            for (int p : primes) {
                while (v % p == 0) {
                    v /= p;
                    fac.put(p, fac.getOrDefault(p, 0) + 1);
                }
            }
        }
        long mod = 1000000007;
        long ans = 1;
        for (var e : fac.values()) {
            ans = (ans * (e + 1)) % mod;
        }
        out.writeln(ans);
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
class BasicScanner {
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public BasicScanner(InputStream in) {this.in = in;}
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buf);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buf[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buf[ptr] && buf[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    private StringBuilder nextSequence() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb;
    }
    public char nextChar() {
        return (char) readByte();
    }
    public String next() {
        return nextSequence().toString();
    }
    public String next(int len) {
        return new String(nextChars(len));
    }
    public char[] nextChars() {
        final StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (33 <= b && b <= 126 && i < len) {s[i++] = (char) b; b = readByte();}
        if (i != len) throw new NoSuchElementException(String.format("length %d is longer than the sequence.", len));
        return s;
    }
    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 = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}


/**
 * @author https://atcoder.jp/users/suisen
 */
class Out {
    private final OutputStream out;
    private byte[] buf = new byte[1024];
    private int ptr = 0;
    private static final int AUTO_FLUSH_THRETHOLD = 1 << 17;

    public Out(OutputStream out) {
        this.out = out;
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (IOException e) {e.printStackTrace();}
    }

    public void close() {
        try {out.close();} catch (IOException e) {e.printStackTrace();}
    }

    public Out writeln() {return write('\n');}
    public Out writeln(Object o) {return write(o).write('\n');}
    public Out writeln(String s) {return write(s).write('\n');}
    public Out writeln(char[] c) {return write(c).write('\n');}
    public Out writeln(char   c) {return write(c).write('\n');}
    public Out writeln(byte   b) {return write(b).write('\n');}
    public Out writeln(int    x) {return write(x).write('\n');}
    public Out writeln(long   x) {return write(x).write('\n');}
    public Out writeln(double d) {return write(d).write('\n');}

    public Out writeSpace() {return write(' ');}
    
    public Out write(Object o) {
        return write(o.toString());
    }

    public Out write(String s) {
        try {
            Field strValueField = s.getClass().getDeclaredField("value");
            strValueField.setAccessible(true);
            byte[] b = (byte[]) strValueField.get(s);
            int l = s.length();
            if (l > AUTO_FLUSH_THRETHOLD) {
                flush();
                int i = 0;
                while (i + AUTO_FLUSH_THRETHOLD < l) {
                    out.write(b, i, AUTO_FLUSH_THRETHOLD);
                    out.flush();
                    i += AUTO_FLUSH_THRETHOLD;
                }
                ensureCapacity(l - i);
                System.arraycopy(b, i, buf, 0, l - i);
                ptr = l - i;
            } else {
                ensureCapacity(ptr + l);
                System.arraycopy(b, 0, buf, ptr, l);
                ptr += l;
            }
        } catch (Exception e) {e.printStackTrace();}
        return this;
    }

    public Out write(char[] c) {
        int l = c.length;
        if (l > AUTO_FLUSH_THRETHOLD) {
            flush();
            ensureCapacity(AUTO_FLUSH_THRETHOLD);
            int i = 0;
            while (i + AUTO_FLUSH_THRETHOLD < l) {
                for (int j = 0; j < AUTO_FLUSH_THRETHOLD; j++) {
                    buf[ptr++] = (byte) c[i + j];
                }
                flush();
                i += AUTO_FLUSH_THRETHOLD;
            }
            for (; i < l; i++) {
                buf[ptr++] = (byte) c[i];
            }
        } else {
            ensureCapacity(ptr + l);
            for (char ch : c) buf[ptr++] = (byte) ch;
        }
        return this;
    }

    public Out write(char c) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = (byte) c;
        return this;
    }

    public Out write(byte b) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = b;
        return this;
    }

    public Out write(int x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(long x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(double d) {
        return write(Double.toString(d));
    }

    private void ensureCapacity(int cap) {
        if (cap > AUTO_FLUSH_THRETHOLD) {
            flush();
        }
        if (cap >= buf.length) {
            int newLength = buf.length;
            while (newLength < cap) newLength <<= 1;
            byte[] newBuf = new byte[newLength];
            System.arraycopy(buf, 0, newBuf, 0, buf.length);
            buf = newBuf;
        }
    }
    private static int stringSize(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
    private static int stringSize(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class ExtendedScanner extends BasicScanner {
    public ExtendedScanner(InputStream in) {super(in);}
    public int[] ints(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> nextInt());
        return a;
    }
    public int[] ints(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
        return a;
    }
    public int[][] ints(final int n, final int m) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m));
        return a;
    }
    public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m, f));
        return a;
    }
    public long[] longs(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> nextLong());
        return a;
    }
    public long[] longs(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
        return a;
    }
    public long[][] longs(final int n, final int m) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m));
        return a;
    }
    public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m, f));
        return a;
    }
    public char[][] charArrays(final int n) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars());
        return c;
    }
    public char[][] charArrays(final int n, final int m) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars(m));
        return c;
    }
    public double[] doubles(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, $ -> nextDouble());
        return a;
    }
    public double[][] doubles(final int n, final int m) {
        final double[][] a = new double[n][];
        Arrays.setAll(a, $ -> doubles(m));
        return a;
    }
    public String[] strings(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next());
        return s;
    }
    public String[] strings(final int n, final int m) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next(m));
        return s;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class MathUtil{
    private static final long UNDER32_MASK = 0xffff_ffffl;
    private MathUtil(){}
    /**
     * Enumarate primes equal to or less than n.
     * @param n
     * @return {@code ArrayList} that holds primes.
     */
    public static ArrayList<Integer> eratosthenes(final int n) {
        final int[] div = eratosthenesDivisors(n);
        final ArrayList<Integer> result = new ArrayList<>();
        for (int i = 2; i <= n; i++) if (div[i] == i) result.add(i);
        return result;
    }
    /**
     * execute eratosthenes's prime-enumerate algorithm. a[i] holds the greatest
     * divisor of i. if a[i] = i, i is a prime number. This arrary enables you to
     * prime-factorize in O(log n) time.
     * @param n
     * @return divisor array.
     */
    public static int[] eratosthenesDivisors(final int n) {
        final int[] divisors = new int[n + 1];
        if (n <= 0) return null;
        for (int i = 1; i <= n; i++) {
            if ((i & 1) != 0) divisors[i] = i;
            else divisors[i] = 2;
        }
        for (int i = 3; i <= n; i += 2) {
            if (divisors[i] == i) for (long j = (long) i * i; j <= n; j += i << 1) divisors[(int) j] = i;
        }
        return divisors;
    }
    /**
     * Caluculate prime-factorization in O(sqrt(n)) time.
     * @param n
     * @return {@code HashMap} of {prime: index}
     */
    public static HashMap<Long, Integer> primeFactorization(long n) {
        final HashMap<Long, Integer> primes = new HashMap<>();
        for (long p = 2; p * p <= n; p++) {
            int q = 0;
            while (n % p == 0) {n /= p; q++;}
            if (q > 0) primes.put(p, q);
        }
        if (n > 1) primes.put(n, 1);
        return primes;
    }
    public static TreeSet<Long> divisors(final long n) {
        final TreeSet<Long> divisors = new TreeSet<>();
        for (long i = 1; i * i <= n; i++) if (n % i == 0) {divisors.add(i); divisors.add(n / i);}
        return divisors;
    }
    private static HashMap<Long, Integer> lcmMap(final HashMap<Long, Integer> amap, final HashMap<Long, Integer> bmap) {
        if (amap.size() < bmap.size()) return lcmMap(bmap, amap);
        final HashMap<Long, Integer> lcm = amap;
        for (final Map.Entry<Long, Integer> e : bmap.entrySet()) {
            final long prime = e.getKey();
            if (lcm.containsKey(prime)) lcm.put(prime, Math.max(lcm.get(prime), e.getValue()));
            else lcm.put(prime, e.getValue());
        }
        return lcm;
    }
    private static HashMap<Long, Integer> lcmMap(final HashMap<Long, Integer> amap, final long b) {
        final HashMap<Long, Integer> bmap = primeFactorization(b);
        return lcmMap(amap, bmap);
    }
    public static HashMap<Long, Integer> lcmMap(final long... a) {
        HashMap<Long, Integer> amap = new HashMap<>();
        for (final long c : a) amap = lcmMap(amap, c);
        return amap;
    }
    /**
     * calculate lcm(a, b) fast. (NOT considering overflow.)
     */
    public static long lcm(final long a, final long b) {return (a / gcd(a, b)) * b;}
    /**
     * Caluculate the GCD of (a, b)
     * @param a first value
     * @param b second value
     * @return GCD(a, b)
     */
    public static long gcd(long a, long b) {
        return positiveGCD(Math.abs(a), Math.abs(b));
    }
    private static long positiveGCD(long a, long b) {
        if (a < b) return positiveGCD(b, a);
        if (b == 0) return a;
        if (a == 0) return b;
        long r = a % b;
        while (r != 0) {a = b; b = r; r = a % b;}
        return b;
    }
    public static long gcd(final long... a) {
        long gcd = 0; for (final long c : a) gcd = gcd(gcd, c);
        return gcd;
    }
    /**
     * Return one of the solutions to {@code ax+by=gcd(a, b)}.
     * 
     * @return {@code x}, {@code y}, {@code gcd(a, b)}.
     * @param a a of ax+by=gcd(a, b).
     * @param b b of ax+by=gcd(a, b).
     */
    public static long[] extGCD(final long a, final long b) {
        final long[] ret = new long[3];
        final long[] xy = new long[2];
        ret[2] = extGCD(a, b, xy);
        ret[0] = xy[0]; ret[1] = xy[1];
        return ret;
    }
    private static long extGCD(final long a, final long b, final long[] xy) {
        if (b == 0) {xy[0] = 1; xy[1] = 0; return a;}
        long tmp = xy[0]; xy[0] = xy[1]; xy[1] = tmp;
        final long d = extGCD(b, a % b, xy);
        tmp = xy[0]; xy[0] = xy[1]; xy[1] = tmp;
        xy[1] -= a / b * xy[0];
        return d;
    }
    /**
     * caluculate a ^ b NOT considering overflow. so if you want to calculate a ^ b
     * (mod p), use ModUtil.pow(a, b).
     * @param a base
     * @param b exponent
     * @return a ^ b
     */
    public static long pow(final int a, long b) {
        long ret = 1l;
        for (long c = 1, ac = a; b > 0; ac *= ac, c <<= 1) if ((-b & b) == c) {ret *= ac; b &= ~(-b & b);}
        return ret;
    }
    /**
     * Caluculate the combination nCr NOT considering overflow.
     * 
     * @param n left
     * @param r right
     * @return nCr
     */
    public static long comb(long n, long r) {
        if (n < r) return 0;
        r = Math.min(r, n - r);
        long res = 1; for (long d = 1; d <= r; d++) {res *= n--; res /= d;}
        return res;
    }
    public static long ceilSqrt(final long n) {
        long l = -1, r = n;
        while (r - l > 1) {
            final long m = (r + l) >> 1;
            if (m * m >= n) r = m;
            else l = m;
        }
        return r;
    }
    public static long floorSqrt(final long n) {
        long l = 0, r = n + 1;
        while (r - l > 1) {
            final long m = (r + l) >> 1;
            if (m * m > n) r = m;
            else l = m;
        }
        return l;
    }
    public static long int2ToLong(final int upper, final int lower) {return ((long) upper << Integer.SIZE) | lower;}
    public static int upper32(final long l) {return (int) (l >>> Integer.SIZE);}
    public static int lower32(final long l) {return (int) (l & UNDER32_MASK);}

    public static BigInteger chineseRemainderTheorem(long[] mod, long[] remainder) {
        int n = mod.length;
        long[] t = new long[n];
        t[0] = remainder[0];
        for (int i = 1; i < n; i++) {
            long c = remainder[i];
            long m = mod[i];
            for (int j = 0; j < i; j++) {
                c -= t[j];
                c *= inv(mod[j], m);
                c %= m;
                if (c < 0) c += m;
            }
            t[i] = c;
        }
        BigInteger res = BigInteger.valueOf(t[n - 1]);
        for (int i = n - 2; i >= 0; i--) {
            res.multiply(BigInteger.valueOf(mod[i])).add(BigInteger.valueOf(t[i]));
        }
        return res;
    }

    public static long inv(long a, final long mod) {
        long b = mod;
        long u = 1, v = 0;
        while (b >= 1) {
            final long t = a / b;
            a -= t * b;
            final long tmp1 = a; a = b; b = tmp1;
            u -= t * v;
            final long tmp2 = u; u = v; v = tmp2;
        }
        u %= mod;
        return u < 0 ? u + mod : u;
    }
}