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.

Examples

Input

3 2
4 1 5

Output

3

Input

13 17
29 7 5 7 9 51 7 13 8 55 42 9 81

Output

6

Input

10 400000000
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output

25

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