Problem Statement

Given an array ~a~ of ~n~ integers ~a_1, a_2, ..., a_n~, as well as an integer ~k~, determine the sum of the subarray which has a sum which is less than or equal to ~k~. There will always be a subarray with a sum of ~0~. If there is no subarray with sum less than or equal to ~k~ then output ~-1~.

Remember that a subarray is a selection of continuous elements of ~a~.

Input Format

Your first line will contain two space-separated integers ~n~ and ~k~. Your next line will contain ~n~ space-separated integers ~a_1, ..., a_n~.

Output Format

You should output the largest subarray sum less than or equal to ~k~. If there is no subarray with sum less than or equal to ~k~ then output ~-1~.

Constraints

• ~1 \leq n \leq 10^5~
• ~-10^9 \leq a_i \leq 10^9~
• ~-10^9 \leq k \leq 10^9~ ## Sample Cases

Input 1

6 13
100 -4 2 7 2 5

Output 1

12

Explanation 2

The subarray with sum of ~12~ is ~[-4, 2, 7, 2, 5]~.

Input 2

5 5
1 2 -4 2 5

Output 2

5

Explanation 2

The subarray with sum of ~5~ is ~[5]~.