We call a sequence of N natural numbers (a1, a2, ..., aN) a P-sequence, if the product of any two adjacent numbers in it is not greater than P. In other words, if a sequence (a1, a2, ..., aN) is a P-sequence, then ai * ai+1 ≤ P ∀ 1 ≤ i < N
You are given N and P. Your task is to find the number of such P-sequences of N integers modulo 109+7.
The first line of input consists of N
The second line of the input consists of P.
2 ≤ N ≤ 103
1 ≤ P ≤ 109
1 ≤ ai
Output the number of P-sequences of N integers modulo 109+7.