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: Runtime Error)

N,x=gets.chomp.split(' ').map{|n| n.to_i}
A=gets.chomp.split(' ').map{|n| n.to_i}
cnt = 0
if(A[0] > x)
	dif = A[0]-x
	A[0] -= dif
	cnt += dif
end
for i in 1..(N-1)
	sum = A[i-1]+A[i]
	if(sum > x)
		dif = sum-x
		A[i] -= dif
		cnt += dif
	end
end
puts cnt