Given a directed graph of N nodes, each node has a value A[i].

There is a directed edge of length 1 from node i to node j if and only if: - | i — j | <= k . The absolute difference between i and j is less than or equal to k. - A[i] > A[j]

For each node X, find B[X] which is the length of the shortest path to a node Y such that A[Y] is a prime number. If there is no way to go to such a node Y then we say that B[X] is 0.

Print the sum of all elements in array B.

Since the answer might be large return it modulo 10^9 + 7.

Constraints

1 <= N <= 10^5 and 1 <= k <= N 1 <= A[i] <= 10^6

Input 1 5 2 2 4 8 16 32

Output 1 6

Input 2 3 1 1 2 4

Output 2 1