Construct Sum from Custom Dice

You are given a set of custom dice. Each die is labeled with a positive integer value, and you have an infinite supply of dice for each given face value. Your task is to determine whether it is possible to obtain a specified target sum by rolling any number of these dice and summing the outcomes.

Formally, given a list of n integers \(A = [a_1, a_2, \dots, a_n]\) and an integer target \(T\), determine if there exist non-negative integers \(x_1, x_2, \dots, x_n\) such that:

[ a_1x_1 + a_2x_2 + \dots + a_nx_n = T ]

If such a combination exists, output YES; otherwise, output NO.

Examples:

• For n = 5, dice faces [1, 2, 3, 5, 7] and T = 12, the answer is YES because \(5+7=12\) or other combinations can work.
• For n = 3, dice faces [3, 5, 7] and T = 1, the answer is NO since no combination of the given numbers can sum to 1.

inputFormat

The first line contains two space-separated integers n and T — the number of available dice faces and the target sum respectively. The second line contains n space-separated integers representing the values on the custom dice faces.

outputFormat

Output a single line containing either YES if the target sum can be constructed using any combination of the dice faces, or NO otherwise.

5 12
1 2 3 5 7

YES