Reservoir Dam Break Risk

A reservoir is operating under high load due to continuous heavy rains. Its water level has exceeded the safe limit, putting it at the verge of a dam break.

Aya is responsible for controlling the reservoir's water level. Based on forecasts from both the meteorological and hydrological departments, she receives the inflow amounts \(a_1, a_2, \dots, a_n\) and the outflow amounts \(b_1, b_2, \dots, b_n\) for the next \(n\) hours. The net inflow for the \(i\)-th hour is defined as:

\(a_i - b_i\)

She believes that if there exists any continuous period of \(k\) hours during which the sum of net inflows is greater than or equal to a threshold \(M\), then there is a possibility of a dam break, which could lead to dangerous flooding downstream.

Your task is to determine whether such a period exists.

inputFormat

The input consists of three lines:

1. The first line contains three integers \(n\), \(k\), and \(M\) separated by spaces.
2. The second line contains \(n\) integers representing the inflow amounts \(a_1, a_2, \dots, a_n\).
3. The third line contains \(n\) integers representing the outflow amounts \(b_1, b_2, \dots, b_n\).

outputFormat

Print a single line: Yes if there exists any continuous segment of \(k\) hours for which the sum of net inflows is at least \(M\); otherwise, print No.

sample

5 2 7
6 5 2 4 1
1 2 1 1 0

Yes