Frisbee

Farmer John and his cows are playing frisbee. Bessie threw the frisbee, it reached Mark, and Mark's team took it. Mark's height is $H$, and $N$ cows from Bessie's team are standing near Mark. Taking the frisbee that Mark throws needs a height greater than or equal to Mark's height. Several cows may build one stack to reach higher. The height of a stack is the sum of the heights of the cows in it.

Every cow has a height, a weight, and a strength. The strength of a cow is the weight it can hold. In a stack, the weight a cow actually holds is the sum of the weights of the cows above it. The safety of a stack is the minimum of (strength $-$ total weight above) taken over the cows in the stack, and it is the extra weight that can be placed on top of the stack.

Bessie's team can pick any subset of the cows and stack them in any order. Decide whether a stack of height at least $H$ can be built, and if it can, find the largest safety such a stack can reach.

The first line contains $N$ and $H$ ($2 \le N \le 20$, $1 \le H \le 10^9$).

Each of the next $N$ lines contains the height, the weight, and the strength of one cow. Every number in the input is a natural number no greater than $10^9$.

If a stack of height at least $H$ can be built, print on one line the maximum safety over all such stacks. When every stack of height at least $H$ already carries more weight than some cow's strength, this value is negative; print the negative value as it is.

If no stack of height at least $H$ can be built, print Mark is too tall without the quotes.