183. Painting the balls

time limit per test: 0.25 sec / memory limit per test: 4096 KB

Petya puts the N white balls in a line and now he wants to paint some of them in black, so that at least two black balls could be found among any M successive balls. Petya knows that he needs Ci milliliters of dye exactly to paint the i-th ball. Your task is to find out for Petya the minimum amount of dye he will need to paint the balls.

Input

The first line contains two integer numbers N and M (2<=N<=10000, 2<=M<=100, M<=N). The second line contains N integer numbers C1, C2, …, CN (1<=Ci<=10000).

Output

Output only one integer number - the minimum amount of dye Petya will need (in milliliters).

Example(s)

Sample Input	Sample Output
6 3 1 5 6 2 1 3	9

Note

Example note: 1, 2, 4, 5 balls must be painted.