You are given an array of N integers. Your task is to find the number of ways of selecting non-empty subsequences of the array such that the absolute difference between any two adjacent elements (if they exist ) of the selected subsequence is not greater than K.

Since, the number of ways can be very large, output it modulo 1000000007.

Note: A subsequence of an array is an ordered subset of the array's elements having the same sequential ordering as the original array.

INPUT FORMAT

• First line of input contains two space separated integers N and K.
• Second line of input contains N space separated integers denoting the N elements of the array.

OUTPUT FORMAT

• Output the number of ways of selecting subsequences following the given condition, modulo 1000000007.

CONSTRAINTS

• 1 ≤ N ≤ 500000
• 0 ≤ K ≤ 10⁹
• -10⁹ ≤ A[i] ≤ 10⁹ , A[i] denotes the i^th element of the array.