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 Kotlin (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = MyScanner()
        val n = sc.nextInt()
        if (n == 1) {
            println(1)
            return
        }

        val prime = mutableListOf<Int>()
        val cnt = mutableListOf<Int>()
        prime.add(2)
        cnt.add(0)
        for (i in 2..n) {
            var t = i
            for (j in prime.indices) {
                while (t % prime[j] == 0) {
                    t /= prime[j]
                    cnt[j]++
                }
            }
            if (t != 1) {
                prime.add(t)
                cnt.add(1)
            }
        }

        var ans = ModInt(1)
        cnt.forEach {
            ans *= (it + 1)
        }

        println(ans)
    }
}

class ModInt(_num: Number) : Number() {
    companion object {
        const val mod: Long = 1000000007L
    }

    private val num: Long = if (_num.toLong() < 0) (_num.toLong() % mod) + mod else _num.toLong() % mod
    operator fun plus(right: Number) = ModInt(num + (right.toLong() % mod))
    operator fun minus(right: Number) = ModInt(num - (right.toLong() % mod))
    operator fun times(right: Number) = ModInt(num * (right.toLong() % mod))

    // modが素数の時のみ
    operator fun div(right: Number) = this * ModInt(right).inverse()

    fun power(n: Number): ModInt {
        var a = this
        var result = ModInt(1)
        var tmp = n.toLong()
        while (tmp > 0) {
            if (tmp % 2 == 1L) {
                result *= a
            }
            tmp /= 2
            a *= a
        }
        return result
    }

    // modが素数のときのみ 逆元
    fun inverse(): ModInt {
        return power(mod - 2L)
    }

    override fun toString() = num.toString()
    override fun toInt() = num.toInt()
    override fun toLong() = num
    override fun toByte() = num.toByte()
    override fun toChar() = num.toChar()
    override fun toDouble() = num.toDouble()
    override fun toFloat() = num.toFloat()
    override fun toShort() = num.toShort()
}

class MyScanner {
    private var ptr = 0
    private var l = listOf<String>()

    fun next(): String {
        while (l.size <= ptr) {
            l = readLine()!!.split(' ')
            ptr = 0
        }
        return l[ptr++]
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextCharArray() = next().toCharArray()
    fun nextChar() = next()[0]

    fun list(): List<String> {
        ptr = l.size
        return readLine()!!.split(' ')
    }

    fun intList() = list().map { s -> s.toInt() }
    fun longList() = list().map { s -> s.toLong() }
    fun doubleList() = list().map { s -> s.toDouble() }

    fun array() = list().toTypedArray()
    fun intArray() = intList().toIntArray()
    fun longArray() = longList().toLongArray()
    fun doubleArray() = doubleList().toDoubleArray()
}