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# Scaler Subarrays II

Problem Description

You are given an array A of size N.

A subarray A [ l ... r ] contains all the elements A[l], A[l+1], .... , A[r]. A subarray A [ l ... r ] is called a scaler subarray if max( A [ l ... r ] ) and A[l] + A[r] are congruent modulo B.

Here, max( A [ l ... r ] ) is the maximum value of this subarray.

Given an integer n > 1, called a modulus, two integers a and b are said to be congruent modulo n, if n is a divisor of their difference (i.e. if there is an integer k such that

a − b = k n).

Find the total number of scaler subarrays of A. Since the answer can be large, return it modulo 109 + 7.

Problem Constraints

1 <= N, B <= 5 x 105

1 <= A[i] <= 109

Input Format

The first argument contains an integer array A of size N.

The second argument contains an integer B.

Output Format

Return the number of scaler subarrays of A modulo 109 + 7.

Example Input

Input 1:

```  A : [ 8, 7 ]
B : 4
```

Input 2:

```  A : [ 4, 5, 3, 8, 8 ]
B : 5
```

Example Output

Output 1:

```  1
```

Output 2:

```  3
```

Example Explanation

Explanation 1:

```  The subarray [8] is scaler because max([8]) = 8 and A[l] + A[r] = 16.
8 and 16 are congruent modulo 4 because 16 - 8 = 8 is divisible by 4.
```

Explanation 2:

```  Scaler subarrays are [5], [5, 3, 8] and [5, 3, 8, 8].
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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