Given a binary string of length ~N~, where exactly ~K~ characters are ones, compute the number of substrings that have at least three ones.

Constraints

~1 \le N \le 10^9~

~0 \le K \le 10^6~

~1 \le a_i \le N~

~a_i~ are presented in sorted order.

~K \le N~

In tests worth ~5~ marks, you may assume ~K \le 10^2~.

In tests worth an additional ~5~ marks, you may assume ~K \le 10^5~.

Input Specification

The first line of the input contains two space-separated integers, ~N~ and ~K~.

Each of the next ~K~ lines contains a single integer, ~a_i~, indicating that character ~a_i~ of the string is a one.

Output Specification

Output a single integer, the number of substrings that contain at least three ones.

Sample Input

5 4
1
2
4
5

Sample Output

3