#P1646A. Square Counting
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ID: 6313
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Square Counting
No submission language available for this problem.
Description
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 $0\leq a_i < n$, 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.
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 $s$ ($1\le n< 10^6$, $0\le s \le 10^{18}$). It is guaranteed that the value of $s$ is a valid sum for some sequence satisfying the above constraints.
For each test case, print one integer — the number of elements in the sequence which are equal to $n^2$.
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 $s$ ($1\le n< 10^6$, $0\le s \le 10^{18}$). 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 $n^2$.
Samples
4
7 0
1 1
2 12
3 12
0
1
3
1
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.