Money Left After Shopping

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

You have m units of money and must buy all n items costing a_i each. If you can afford them print YES and the balance, otherwise NO and the additional amount required.

Input

First n m, followed by n item prices a_i.

Output

Print YES d with nonnegative remaining balance, otherwise NO d with nonnegative shortage.

Subtasks

• Subtask 1 (20%): n ≤ 10, prices/budget 0..100.

• Subtask 2 (30%): n ≤ 1000, prices/budget 0..10^6.

• Subtask 3 (50%): n ≤ 100000, prices/budget 0..10^9.

Examples

Example 1

Input:

3 20
5 8 9

Output:

NO 2

Explanation: Total price is 22; the shortage is 2.

Example 2

Input:

2 10
4 6

Output:

YES 0

Explanation: The budget exactly matches the price.

Example 3

Input:

0 0

Output:

YES 0

Explanation: Buying zero items with zero budget is sufficient.