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:T6fb,

Taisia has $$$n$$$ six-sided dice. Each face of the die is marked with a number from $$$1$$$ to $$$6$$$, each number from $$$1$$$ to $$$6$$$ is used once.

Taisia rolls all $$$n$$$ dice at the same time and gets a sequence of values $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 6$$$), where $$$a_i$$$ is the value on the upper face of the $$$i$$$-th dice. The sum of this sequence is equal to $$$s$$$.

Suddenly, Taisia's pet cat steals exactly one dice with maximum value $$$a_i$$$ and calculates the sum of the values on the remaining $$$n-1$$$ dice, which is equal to $$$r$$$.

You only know the number of dice $$$n$$$ and the values of $$$s$$$, $$$r$$$. Restore a possible sequence $$$a$$$ that fulfills the constraints.

Input

The first line contains the integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of testcases.

Each testcase is given on a separate line and contains three integers $

Taisia and Dice

Examples