Problem 39: Subarray Sum Equals K

Problem Statement: Given an array of n integers and an integer k, count the number of contiguous subarrays that sum to k.

Input

The first line contains two integers n and k. The second line contains n space-separated integers.

Output

Print the number of subarrays whose sum equals k.

Examples


Input:
5 5
1 2 3 2 1

Output:
2

Solution Explanation

Method 1: Use a prefix sum array combined with a hash map to count the frequency of prefix sums and thereby count the number of valid subarrays in O(n) time. Method 2: A brute-force approach by checking all subarrays leads to O(n^2) time, which is only feasible for small arrays.

Solution in C++


#include 
#include 
#include 
using namespace std;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, k; cin >> n >> k;
    vector a(n);
    for (int i=0; i> a[i];

    unordered_map mp;
    mp[0] = 1;
    int prefix = 0; 
    long long ans = 0;
    for (int i=0; i