Even Distribution of Packages

You are given N packages with specified weights, and M trucks, each capable of carrying at most W units of weight. The task is to determine whether it is possible to distribute all packages among the trucks so that:

• The total weight of the packages is evenly divided among the trucks.
• No truck carries a weight that exceeds its maximum capacity W.

Mathematically, if \(T = \sum_{i=1}^{N} weight_i\), then each truck must carry exactly \(\frac{T}{M}\) weight (with \(T\) divisible by \(M\)) and it must hold that \(\frac{T}{M} \le W\). You need to decide if such a distribution is possible.

inputFormat

The input is read from standard input and has the following format:

N
w1 w2 ... wN
M W

Where:

• N is the number of packages.
• w1, w2, ..., wN are the weights of the packages.
• M is the number of trucks.
• W is the maximum capacity of each truck.

outputFormat

Output a single line to standard output containing either yes if it is possible to distribute the packages evenly under the given constraints or no otherwise.

4
2 4 6 8
2 10

yes