The SDOI in $2045$ is far from what it was been $30$ years ago. Each competition has $t$ minutes and $n$ problems.
The $ith$ problem with the original mark of $A_i(A_i \leq 10^{6})$,and it decreases $B_i$ by each minute. It is guaranteed that it does not go to minus when the competition ends. For example someone solves the $ith$ problem after $x$ minutes of the competition beginning. He/She will get $A_i-B_i * x$ marks.
If someone solves a problem on $x$ minute. He/She will begin to solve the next problem on $x+1$ minute.
dxy who attend this competition with excellent strength, can measure the time of solving each problem exactly.He will spend $C_i(C_i \leq t)$ minutes to solve the ith problem. It is because he is so godlike that he can solve every problem of this competition. But to the limitation of time, it's probable he cannot solve every problem in this competition. He wanted to arrange the order of solving problems to get the highest mark in this competition.
Input
There is an positive integer $T(T \leq 10)$ in the first line for the number of testcases.(the number of testcases with $n>200$ is no more than $5$)
For each testcase, there are two integers in the first line $n(1 \leq n \leq 1000)$ and $t(1 \leq t \leq 3000)$ for the number of problems and the time limitation of this competition.
There are $n$ lines followed and three positive integers each line $A_i, B_i, C_i$. For the original mark,the mark decreasing per minute and the time dxy of solving this problem will spend.
Output
For each testcase output a line for an integer, for the highest mark dxy will get in this competition.
Sample Input
1
4 10
110 5 9
30 2 1
80 4 8
50 3 2
Sample Output
88
Hint:
First to solve problem $2$ and then solve problem $1$ he will get $88$ marks. Higher than any other order.
