Day8 - C - Another Problem on Strings CodeForces - 165C

A string is binary, if it consists only of characters "0" and "1".

String v is a substring of string w if it has a non-zero length and can be read starting from some position in string w. For example, string "010" has six substrings: "0", "1", "0", "01", "10", "010". Two substrings are considered different if their positions of occurrence are different. So, if some string occurs multiple times, we should consider it the number of times it occurs.

You are given a binary string s. Your task is to find the number of its substrings, containing exactly k characters "1".

Input

The first line contains the single integer k (0 ≤ k ≤ 10⁶). The second line contains a non-empty binary string s. The length of s does not exceed 10⁶ characters.

Output

Print the single number — the number of substrings of the given string, containing exactly k characters "1".

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

1
1010

Output

6

Input

2
01010

Output

4

Input

100
01010

Output

0

Note

In the first sample the sought substrings are: "1", "1", "10", "01", "10", "010".

In the second sample the sought substrings are: "101", "0101", "1010", "01010".

思路：依旧是双指针，和前两题无差，特判一下k=0的情况，左指针可以小优化一下，将连续的0对右指针只计算一次

typedef long long LL;
typedef pair<LL, LL> PLL;

const int maxm = 1e6+5;

int k;
char buf[maxm];

int main() {
    ios::sync_with_stdio(false), cin.tie(0);
    cin >> k >> buf;
    LL ans = 0;
    int n = strlen(buf);
    LL num = 0;
    int l = 0, r = 0, t = 0, r1 = 0;
    if(k == 0) {
        for(int i = 0; i < n; ++i) {
            if(buf[i] == '0')
                num++;
            else {
                ans += (LL)(num*(num+1) / 2);
                num = 0;
            }
        }
        ans += (LL)(num*(num+1) / 2);
    } else {
        if(buf[r] == '1') t++;
        while(l < n) {
            while(r < n) {
                if(t == k) break;
                r++;
                if(buf[r] == '1') t++;
            }
            if(r >= n) break;
            if(r1 <= r) {
                r1 = r+1;
                while(r1 < n && buf[r1] == '0') r1++;
            }
            LL L = 1;
            while(buf[l++] == '0') L++;
            ans += (LL)(r1 - r) * L;
            t--;
        }
    }
        
    cout << ans << "\n";
    return 0;
}

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