Yet Another Coin Problem

There are $N$ kinds of coins. The $i$-th kind has $C_i$ coins, and each coin is worth $V_i$ won. $(1 \le i \le N)$ Can you choose some coins so that their values sum to exactly $X$ won? If it is possible, print one way to do it.

The first line contains the number of test cases $T$. $(1 \le T \le 100)$

The first line of each test case contains $N$ and $X$, separated by a space. $(1 \le N \le 50; 1 \le X \le 10^{18})$

Each of the next $N$ lines contains $C_i$ and $V_i$, separated by a space. Within one test case, all $V_i$ are distinct. $(1 \le C_i \le 10^{12}; 1 \le V_i \le 500\,000)$

The sum of $N$ over all test cases does not exceed $500$, and the sum of all $V_i$ does not exceed $500\,000$.

For each test case, print YES if you can choose coins so that their values sum to exactly $X$ won, and NO otherwise. If you print YES, print a second line with $N$ integers $A_1, \cdots, A_N$ separated by spaces. They must satisfy the following conditions.

• $0 \le A_i \le C_i$ $(1 \le i \le N)$
• $A_1V_1 + A_2V_2 + \cdots + A_NV_N = X$