There are ~N~ people in a line buying tickets, where the person at index ~0~ is at the front of the line and index ~N-1~ is at the back of the line. Every person ~i~ (0-indexed) would like to buy ~a_i~ tickets.

Each person takes exactly ~1~ second to buy a ticket, and only one ticket at a time. After purchasing a ticket, they have to go to the end of the line (which takes ~0~ seconds) to buy more tickets. A person leaves the line entirely when they have no more tickets to buy. Find the time it takes for the person initially at position ~K~ (0-indexed) to finish buying tickets.

Input Specification

The first line of input will contain two space-separated integers ~N~ and ~K~, representing the number of people in the line and the initial index of the person.

The second line of input will contain ~N~ space-separated integers ~a_i~, representing the number of tickets each person would like to buy.

Output Specification

Output one integer, representing the time it takes for the person originally at ~K~ to finish buying their tickets.

Constraints

~1 \le N \le 2 \times 10^5~

~0 \le K \le N-1~

~1 \le a_i \le 100~

Sample Input 1

4 0
5 1 1 1

Sample Output 1

8

Sample Explanation

The queue starts at person ~0~, which moves to the back of the line after 1 second (array: ~[1,1,1,4]~).

After another ~3~ seconds, the array will be ~[4]~ (the person ~0~ still needs to purchase 4 tickets).

After another ~4~ seconds, the array will be empty. In total, it took ~1 + 3 + 4 = 8~ seconds.

Sample Input 2

3 2
2 3 2

Sample Output 2

6