13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6da,

For an array $$$a = [a_1, a_2, \dots, a_n]$$$, let's denote its subarray $$$a[l, r]$$$ as the array $$$[a_l, a_{l+1}, \dots, a_r]$$$.

For example, the array $$$a = [1, -3, 1]$$$ has $$$6$$$ non-empty subarrays:

$$$a[1,1] = [1]$$$;
$$$a[1,2] = [1,-3]$$$;
$$$a[1,3] = [1,-3,1]$$$;
$$$a[2,2] = [-3]$$$;
$$$a[2,3] = [-3,1]$$$;
$$$a[3,3] = [1]$$$.

You are given two integers $$$n$$$ and $$$k$$$. Construct an array $$$a$$$ consisting of $$$n$$$ integers such that:

all elements of $$$a$$$ are from $$$-1000$$$ to $$$1000$$$;
$$$a$$$ has exactly $$$k$$$ subarrays with positive sums;
the rest $$$\dfrac{(n+1) \cdot n}{2}-k$$$ subarrays of $$$a$$$ have negative sums.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 5000$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$n$$$ an

Sum on Subarrays

Examples