Exact sum + hash map (Prefix Sum Sub-pattern)

// Count subarrays whose sum is exactly k. Works with negatives and zeros.
long long countSubarrays(vector<int>& nums, int k) {
    unordered_map<long long, int> seen;  // prefix total -> how many times it appeared
    seen[0] = 1;                         // the empty prefix, for ranges starting at index 0
    long long prefix = 0, count = 0;
    for (int x : nums) {
        prefix += x;
        auto it = seen.find(prefix - k); // an earlier total that leaves exactly k between us
        if (it != seen.end()) count += it->second;
        seen[prefix]++;                  // insert AFTER the lookup
    }
    return count;
}