Taco: Making Strictly Increasing Sequence

You are given an integer sequence of length \(n\) and a non-negative integer \(k\) representing the maximum number of operations allowed. In one operation, you can add 1 to any element of the sequence. Your task is to determine whether it is possible to make the sequence strictly increasing by performing at most \(k\) operations.

A sequence \(a_1, a_2, \dots, a_n\) is strictly increasing if and only if \(a_1 < a_2 < \dots a_{i-1}\).

Determine if the total number of increments needed does not exceed \(k\). If it is possible, print YES; otherwise, print NO.

inputFormat

The first line contains an integer \(T\) (the number of test cases). The description of the test cases follows.

For each test case:

• The first line contains two integers \(n\) and \(k\) separated by a space.
• The second line contains \(n\) integers, representing the elements of the sequence.

outputFormat

For each test case, output a single line containing YES if it is possible to transform the sequence into a strictly increasing sequence with at most \(k\) operations, or NO otherwise.

## sample

5
5 3
1 2 2 3 4
4 1
1 3 2 4
4 0
1 2 3 4
3 1000
1000000000 1000000000 1000000000
6 5
1 2 1 2 1 2

YES
NO
YES
YES
NO

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