Coin Combination Problem II

You have N coins each of which has a value a_i. Find the number of combinations that result when you choose K different coins in such a way that the total value of the coins is greater than or equal to L and less than or equal to R.

Constraints

• 1 ≤ K ≤ N ≤ 40
• 1 ≤ a_i ≤ 10¹⁶
• 1 ≤ L ≤ R ≤ 10¹⁶
• All input values are given in integers

Input

The input is given in the following format.

N K L R
a1 a2 ... aN

Output

Print the number of combinations in a line.

Sample Input 1

2 2 1 9
5 1

Sample Output 1

1

Sample Input 2

5 2 7 19
3 5 4 2 2

Sample Output 2

5

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