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.

Square Counting

Examples