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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'prime'

n = gets.to_i
def nPk(n, k)
  r = 1
  while k > 0
    r *= n
    n -= 1
    k -= 1
  end
  r
end
def nCk(n, k)
  r, j = 1, 1
  return 0 if k > n || k < 0
  k = n - k if n - k < k
  while j <= k
    r *= n
    n -= 1
    r /= j
    j += 1
  end
  r
end
x = nPk(n, n)
M = 10 ** 9 + 7
y = Prime.prime_division(x).to_h
z = y.values.map{|i| (i + 1) % M}.inject{|u, v| u * v % M}
puts z