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.

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