Factory Widget Production Goal

A factory operates a number of machines each day to produce widgets. The production capacity of each machine is given by its efficiency. Over a working day lasting H hours, the total number of widgets produced is equal to the sum of all machine efficiencies multiplied by the number of operating hours.

You are given the number of machines N, the number of operating hours H, the production goal C, and a list of efficiencies of the machines. Your task is to determine whether the factory meets or exceeds the production goal.

Formally, let \(E = \sum_{i=1}^{N} e_i\). The factory meets the goal if and only if \(E \times H \ge C\). Otherwise, it does not.

inputFormat

The first line contains three integers separated by spaces: N, H, and C. The second line contains N integers separated by spaces, representing the efficiency of each machine.

outputFormat

Output a single line containing 'Yes' if the factory meets or exceeds the production goal, and 'No' otherwise.## sample

5 8 1000
10 20 30 40 50

Yes