Good Path Verification

You are given a collection of N integers along with three additional integers: S, E, and X. Your task is to determine whether the subarray (or "path") from index S to E (1-indexed) satisfies the following conditions:

1. The subarray is non-decreasing. That is, for all indices \( i \) where \( S \leq i < E \), the condition \( a_i \leq a_{i+1} \) holds.

2. The sum of the elements in the subarray is at least \( X \), i.e., \( \sum_{i=S}^{E} a_i \geq X \).

If both conditions are met, output YES; otherwise, output NO.

inputFormat

The first line contains four space-separated integers: N, S, E, and X.

The second line contains N space-separated integers representing the collection.

outputFormat

Output a single line containing YES if the subarray from S to E is non-decreasing and its sum is at least X; otherwise, output NO.

## sample

6 2 5 10
1 2 3 4 5 6

YES

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