For two positive integers $$$x,y$$$,define $$$con(x,y)$$$ as the number obtained by connecting the decimal representation of $$$x$$$ with $$$y$$$, where $$$x$$$ is on the left and $$$y$$$ is on the right.For example $$$con(20,23)=2023,con(2,33)=233$$$.
You're given two integers $$$n,k$$$.You can choose an array $$$a$$$ of positive integers of size $$$n$$$,which satisfies $$$\Sigma_{i=1}^{n}a_i=k$$$.
Define the score as the number of prime numbers among all $$$con(a_i, a_j)(1\leq i,j\leq n)$$$.Find the minimum score you can get.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.
The only line of each test case contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le k \le 10^9$$$).
For each test case, output a single integer — the minimum score you can get.
62 32 53 33 73 171 1000000000
1 1 9 2 0 0
Test Case $$$1$$$:
One of the optimal array $$$a$$$ is $$$[1,2]$$$.
For this array,$$$con(a_1,a_1)=11,con(a_1,a_2)=12,con(a_2,a_1)=21,con(a_2,a_2)=22$$$.
There's only one prime.It can be proven that $$$1$$$ reaches the minimum.
Test Case $$$2$$$:
One of the optimal array $$$a$$$ is $$$[2,3]$$$.
For this array,$$$con(a_1,a_1)=22,con(a_1,a_2)=23,con(a_2,a_1)=32,con(a_2,a_2)=33$$$.
There's only one prime.It can be proven that $$$1$$$ reaches the minimum.
Test Case $$$3$$$:
The only array $$$a$$$ you can choose is $$$[1,1,1]$$$.
For this array,$$$con(a_i,a_j)=11$$$ for all $$$1 \le i,j \le n$$$.
There're $$$9$$$ primes.It can be proven that $$$9$$$ reaches the minimum.
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