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

$1 \le T \le 10$

$1 \le N \le 10^5$

$1 \le P \le 10^{15}$

$1 \le H_i \le 10^9$