There is an empty matrix $$$M$$$ of size $$$n\times m$$$.

Zhongkao examination is over, and Daniel would like to do some puzzle games. He is going to fill in the matrix $$$M$$$ using permutations of length $$$m$$$. That is, each row of $$$M$$$ must be a permutation of length $$$m^\dagger$$$.

Define the value of the $$$i$$$-th column in $$$M$$$ as $$$v_i=\operatorname{MEX}(M_{1,i},M_{2,i},\ldots,M_{n,i})^\ddagger$$$. Since Daniel likes diversity, the beauty of $$$M$$$ is $$$s=\operatorname{MEX}(v_1,v_2,\cdots,v_m)$$$.

You have to help Daniel fill in the matrix $$$M$$$ and maximize its beauty.

$$$^\dagger$$$ A permutation of length $$$m$$$ is an array consisting of $$$m$$$ distinct integers from $$$0$$$ to $$$m-1$$$ in arbitrary order. For example, $$$[1,2,0,4,3]$$$ is a permutation, but $$$[0,1,1]$$$ is not a permutation ($$$1$$$ appears twice in the array), and $$$[0,1,3]$$$ is also not a permutation ($$$m-1=2$$$ but there is $$$3$$$ in the array).

$$$^\ddagger$$$ The $$$\operatorname{MEX}$$$ of an array is the smallest non-negative integer that does not belong to the array. For example, $$$\operatorname{MEX}(2,2,1)=0$$$ because $$$0$$$ does not belong to the array, and $$$\operatorname{MEX}(0,3,1,2)=4$$$ because $$$0$$$, $$$1$$$, $$$2$$$ and $$$3$$$ appear in the array, but $$$4$$$ does not.

Input

The first line of input contains a single integer $$$t$$$ ($$$1\le t\le 1000$$$) — the number of test cases. The description of test cases follows.

The only line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1\le n,m\le 2\cdot 10^5$$$) — the size of the matrix.

It is guaranteed that the sum of $$$n\cdot m$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, in the first line output a single integer — the maximum beauty of $$$M$$$.

Then output the matrix $$$M$$$ of size $$$n\times m$$$ — the matrix you find.

If there are multiple solutions, you may output any of them.

Note

In the first test case:

$$$v_1=\operatorname{MEX}(1,0,1,0)=2$$$;
$$$v_2=\operatorname{MEX}(0,2,0,2)=1$$$;
$$$v_3=\operatorname{MEX}(2,1,2,1)=0$$$.

Therefore, $$$s=\operatorname{MEX}(2,1,0)=3$$$.

It can be shown that $$$3$$$ is the maximum possible beauty of $$$M$$$.

In the second test case, any permutation will make $$$s=2$$$.

In the third test case:

$$$v_1=\operatorname{MEX}(3,5,1,4,4,2)=0$$$;
$$$v_2=\operatorname{MEX}(0,2,3,1,2,4)=5$$$;
$$$v_3=\operatorname{MEX}(1,1,2,3,5,0)=4$$$;
$$$v_4=\operatorname{MEX}(4,0,4,2,3,5)=1$$$;
$$$v_5=\operatorname{MEX}(2,4,5,5,0,1)=3$$$;
$$$v_6=\operatorname{MEX}(5,3,0,0,1,3)=2$$$.

Therefore, $$$s=\operatorname{MEX}(0,5,4,1,3,2)=6$$$.

Fill in the Matrix

Examples