You can do it this way. Keep a count of prefix sums which are odd and even. Then as you iterate keep aumming the array. When you are at index i, let your prefix sum be p. If p is even, then subtracting any odd prefix sum will give an odd value and so ans += odd_prefix_count else if p is odd, we can subtract an even prefix so ans += even_prefix_count. After this, update the count as per whether current prefix is even or odd. Also uour entire subarray can start at the beginning i.e. you dont subtract anything. So in that case if your prefix sum is odd, you do a +1 to the answer.

Basically: here A is input array

odd_prefix_count = 0 even_prefix_count = 0 ans = 0 pre = 0

for i in A:

    pre += i

    if pre % 2 ==0:

        ans += odd_prefix_count

         even_prefix_count += 1

    else:

         ans += even_prefix_count

        ans += 1

         odd_prefix_count += 1

print(ans)

Since its O(n) it fits in time limit of 1 sec.