CF1575C.Cyclic Sum

The first line contains three integers $n$ , $m$ , and $k$ ( $1 \leq n, m, k \leq 2 \cdot 10^5$ , $k = 1$ or $k$ is a prime number).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \leq a_i \leq 2 \cdot 10^5$ ).

Output an integer denoting the number of different segments in $b$ where the sum of elements in the segment is divisible by $k$ , modulo $10^9 + 7$ .

In the first example, all valid segments are $[1,4]$ , $[2, 3]$ , $[3, 5]$ , and $[4, 2]$ .

In the second example, one of the valid segments is $[1, 5]$ .

In the first example, all valid segments are $[1,4]$ , $[2, 3]$ , $[3, 5]$ , and $[4, 2]$ .

In the second example, one of the valid segments is $[1, 5]$ .