【分糖果】

这是一道英文题，欢迎大家尝试。

Problem Statement

There are NN boxes arranged in a row from left to right. The ii-th box from the left contains A_iAi​ candies.

You will take out the candies from some consecutive boxes and distribute them evenly to MM children.

Such being the case, find the number of the pairs (l, r)(l,r) that satisfy the following:

• ll and rr are both integers and satisfy 1 \leq l \leq r \leq N1≤l≤r≤N.
• A_l + A_{l+1} + ... + A_rAl​+Al+1​+...+Ar​ is a multiple of MM.

Constraints

• All values in input are integers.
• 1 \leq N \leq 10^51≤N≤105
• 2 \leq M \leq 10^92≤M≤109
• 1 \leq A_i \leq 10^91≤Ai​≤109

Input

Input is given from Standard Input in the following format:

NN MMA_1A1​ A_2A2​ ...... A_NAN​

Output

Print the number of the pairs (l, r)(l,r) that satisfy the conditions.

Note that the number may not fit into a 3232-bit integer type.

Sample 1

Inputcopy	Outputcopy
3 2 4 1 5	3

The sum A_l + A_{l+1} + ... + A_rAl​+Al+1​+...+Ar​ for each pair (l, r)(l,r) is as follows:

• Sum for (1, 1)(1,1): 44
• Sum for (1, 2)(1,2): 55
• Sum for (1, 3)(1,3): 1010
• Sum for (2, 2)(2,2): 11
• Sum for (2, 3)(2,3): 66
• Sum for (3, 3)(3,3): 55

Among these, three are multiples of 22.

Sample 2

Inputcopy	Outputcopy
13 17 29 7 5 7 9 51 7 13 8 55 42 9 81	6

Sample 3

Inputcopy	Outputcopy
10 400000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000	25