# Program to find number of consecutive subsequences whose sum is divisible by k in Python

Suppose we have an array nums and a value k. We have to find number of consecutive subsequences whose sum is divisible by k.

So, if the input is like k = 3 nums = [1,2,3,4,1], then the output will be 4 because the subsequences are [3], [1,2], [1,2,3] and [2,3,4].

To solve this, we will follow these steps −

• x := An array of size k and fill with 0
• x[0] := 1
• r:= 0, s:= 0
• for each elem in nums, do
• s :=(s + elem) mod k
• r := r + x[s]
• x[s] := x[s] + 1
• return r

## Example

Let us see the following implementation to get better understanding −

def solve(k, nums):
x = [0]*k
x[0] = 1
r=s=0
for elem in nums:
s = (s+elem) % k
r += x[s]
x[s] += 1
return r

k = 3
nums = [1,2,3,4,1]
print(solve(k, nums))

## Input

3, [1,2,3,4,1]


## Output

4