Source: Codeforces 985D - Sand Fortress

Statement

You build sand pillars on infinitely many positions numbered from left to right. You have n indivisible packs of sand. If position i receives h_i packs, its height is h_i.

There is a fence of height H immediately to the left of position 1, so the first pillar must satisfy h_1 <= H. Adjacent pillars must differ in height by at most 1, and all n packs must be used.

Find the minimum possible number of positions whose height is positive.

Input

One line contains n and H.

Output

Print the minimum number of occupied positions.

Constraints

1 <= n, H <= 10^18

5 2

3

6 8

3