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: Accepted)

MOD = 10**9+7
MAX = 10**3

N = gets.to_i

sieve = [false, false]+[true]*(MAX-1)
$minFactor = [-1]*(MAX+1)

2.step(MAX) do |i|
    if sieve[i]
        $minFactor[i] = i
        (i*2).step(MAX, i) do |j|
            sieve[j] = false
            $minFactor[j] = i if $minFactor[j] < 0
        end
    end
end

def prime_factor n, a
    m = n
    while $minFactor[m] > 0 do
        a << $minFactor[m]
        m /= $minFactor[m]
    end
    return n-1 > 1 ? prime_factor(n-1, a) : a
end

if N == 1
    p 1
else
    p prime_factor(N, []).group_by(&:itself).map{|_,v| v.count + 1}.inject{|pr, c| (pr * c) % MOD}
end