There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies. You will take out the candies from some consecutive boxes and distribute them evenly to M children. Such being the case, find the number of the pairs (l, r) that satisfy the following:

• l and r are both integers and satisfy 1 \leq l \leq r \leq N.
• A_l + A_{l+1} + ... + A_r is a multiple of M.

-----Constraints-----

• All values in input are integers.
• 1 \leq N \leq 10^5
• 2 \leq M \leq 10^9
• 1 \leq A_i \leq 10^9

-----Input----- Input is given from Standard Input in the following format: N M A_1 A_2 ... A_N

-----Output----- Print the number of the pairs (l, r) that satisfy the conditions. Note that the number may not fit into a 32-bit integer type.

-----Sample Input----- 3 2 4 1 5

-----Sample Output----- 3

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

• Sum for (1, 1): 4
• Sum for (1, 2): 5
• Sum for (1, 3): 10
• Sum for (2, 2): 1
• Sum for (2, 3): 6
• Sum for (3, 3): 5 Among these, three are multiples of 2.