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# Binary Subarrays With Sum

In an array `A` of `0`s and `1`s, how many **non-empty** subarrays have sum `S`?

**Example 1:**

```
Input: A = [1,0,1,0,1], S = 2
Output: 4
Explanation: 
The 4 subarrays are bolded below:
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]
```

**Note:**

1. `A.length <= 30000`
2. `0 <= S <= A.length`
3. `A[i]` is either `0` or `1`.

```java
class Solution {
    public int numSubarraysWithSum(int[] A, int S) {
        return atMost(A, S) - atMost(A, S - 1);
    }

    // Using at most sum -> S function
    public int atMost(int[] A, int S) {
        if (S < 0)
            return 0;
        int ans = 0, start = 0, currSum = 0;
        for (int end = 0; end < A.length; end++) {
            currSum += A[end];
            while (currSum > S)
                currSum -= A[start++];
            ans += end - start + 1;
        }
        return ans;
    }
}
```