Dadas's Ramen Mukbang

Dadas is going to eat $N$ bowls of ramen one by one. Fully cooking the $i$-th bowl takes $A_i$ units of time.

For each bowl, Dadas waits for at most $K$ units of time. Therefore, the actual waiting time before eating the $i$-th bowl is $\min(A_i,K)$. Eating takes $0$ time, and only one bowl is prepared at a time.

Thus, the total time until all bowls are eaten is

It is guaranteed that there exists at least one positive integer $K$ for which the total time is exactly $L$. Find the minimum such $K$.

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$N\ L$ $A_1\ A_2\ \cdots\ A_N$

For each test case, print the minimum positive integer $K$ satisfying the condition on one line.

• $1 \le T \le 200\,000$.
• $1 \le N \le 200\,000$.
• $1 \le A_i \le 10^{13}$ ($1 \le i \le N$).
• $1 \le L \le 2 \cdot 10^{18}$.
• The sum of $N$ over all test cases does not exceed $200\,000$.
• For every test case, there exists at least one positive integer $K$ satisfying $\sum_{i=1}^N \min(A_i,K)=L$.