**Time limit:**1.00 s**Memory limit:**512 MB

There are n people who want to get to the top of a building which has only one elevator. You know the weight of each person and the maximum allowed weight in the elevator. What is the minimum number of elevator rides?

# Input

The first input line has two integers n and x: the number of people and the maximum allowed weight in the elevator.

The second line has n integers w_1,w_2,\dots,w_n: the weight of each person.

# Output

Print one integer: the minimum number of rides.

# Constraints

- 1 \le n \le 20
- 1 \le x \le 10^9
- 1 \le w_i \le x

# Example

Input:

4 10 4 8 6 1

Output:

2