Get Minimum Dock Bays

Trucks must start unloading in input order, and a free dock immediately takes the next truck; trucks that start at the same time are assigned in input order. All trucks must finish within time T; find the minimum number of docks. Trucks cannot be reordered.

输入格式

The first line contains n T; the second line contains each truck's duration. 1≤n≤50000, 1≤T≤10^15, 1≤duration≤min(T,10^9). The source has a note about reading the upper bound of T; this site explicitly uses 10^15.

输出格式

Output a single integer, the answer.

样例 1

输入：

5 8
3 4 3 2 3

输出：

3

样例 2

输入：

3 7
2 3 1

输出：

1

样例 3

输入：

2 2
2 2

输出：

2

样例说明

The answers are 3, 1 and 2. In the first example two docks would need 9 minutes, which does not meet the limit of 8.