Alice and Bob saw a challenging track which consists of $$N$$ hurdles of variable heights $$H_i$$. Now, Bob challenges Alice to complete this track with a given amount of jump power $$P$$.

The rules for completing the challenge are as follows:

$$1$$. Each time Alice jumps a hurdle, jump power $$P$$ of Alice reduces by the height of the hurdle.

$$2$$. Every even minute all the remaining hurdles having even heights will decay and their heights reduce by $$1$$ and every odd minute all the remaining hurdles having odd heights will decay and their heights reduce by $$1$$.

Initially, time $$T = 0$$ minute. It takes $$1$$ minute for Alice to reach to the next hurdle and the time taken to jump a hurdle can be considered to be negligible. Alice has to complete the challenge starting from the first hurdle to the last hurdle, left to right, sequentially.

If $$P < 0$$ at any moment, Alice cannot move further. Find out if Alice can complete the challenge?

Input Format

The first line of the input contains $$T$$, the total number of test cases.

The second line of the input contains two space-separated integers $$N$$ and $$P$$, the total number of hurdles and the total jump power value.

The next line contains $$N$$ space-separated integers $$H_i$$, the heights of each hurdle.

Output Format

For each test case, if it is possible for Alice to complete the challenge, print $$Yes$$ and the remaining value of jump power $$P$$ or $$No$$ if it is not possible.

Constraints

\(1 \le T \le 10\)

\(1 \le N \le 10^5\)

\(1 \le P \le 10^{15}\)

\(1 \le H_i \le 10^9\)