int birthday(vector<int> s, int d, int m) {
    std::vector<int>::iterator left = s.begin();
    std::vector<int>::iterator right = left + m; // points behind sliding window
    
    int sum = std::accumulate(left, right, 0);
    int numWays = sum == d ? 1 : 0;
    
    while (right != s.end()) {
        sum = sum - *left + *right; // update sum
        left++; right++; // and move the sliding window
        
        if (sum == d)
            numWays++;
    }
    
    return numWays;
}