Luis has a sequence of $n+1$ integers $a_1, a_2, \ldots, a_{n+1}$. For each $i = 1, 2, \ldots, n+1$ it is guaranteed that $0\leq a_i \lt n$, or $a_i=n^2$. He has calculated the sum of all the elements of the sequence, and called this value $s$.

Luis has lost his sequence, but he remembers the values of $n$ and $s$. Can you find the number of elements in the sequence that are equal to $n^2$?

We can show that the answer is unique under the given constraints.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 2\cdot 10^4$). Description of the test cases follows.

The only line of each test case contains two integers $n$ and $s$ ($1\le n \lt 10^6$, $0\le s \le 10^{18}$). It is guaranteed that the value of $s$ is a valid sum for some sequence satisfying the above constraints.

Output

For each test case, print one integer — the number of elements in the sequence which are equal to $n^2$.

Note

In the first test case, we have $s=0$ so all numbers are equal to $0$ and there isn't any number equal to $49$.

In the second test case, we have $s=1$. There are two possible sequences: $[0, 1]$ or $[1, 0]$. In both cases, the number $1$ appears just once.

In the third test case, we have $s=12$, which is the maximum possible value of $s$ for this case. Thus, the number $4$ appears $3$ times in the sequence.

Samples

4
7 0
1 1
2 12
3 12

0
1
3
1