It is well known that quick sort works by randomly selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. But Jellyfish thinks that choosing a random element is just a waste of time, so she always chooses the first element to be the pivot. The time her code needs to run can be calculated by the following pseudocode:

Now you want to show her that her code is slow. When the function $\mathrm{fun(A)}$ is greater than or equal to $lim$, her code will get $\text{Time Limit Exceeded}$. You want to know how many distinct permutations $P$ of $[1, 2, \dots, n]$ satisfies $\mathrm{fun(P)} \geq lim$. Because the answer may be large, you will only need to find the answer modulo $10^9+7$.

Input

The only line of the input contains two integers $n$ and $lim$ ($1 \leq n \leq 200$, $1 \leq lim \leq 10^9$).

Output

Output the number of different permutations that satisfy the condition modulo $10^9+7$.

见题面 Input 部分

见题面 Output 部分

In the first example, $P = [1, 4, 2, 3]$ satisfies the condition, because: $\mathrm{fun([1, 4, 2, 3]) = 4 + fun([4, 2, 3]) = 7 + fun([2, 3]) = 9 + fun([3]) = 10}$

Do remember to output the answer modulo $10^9+7$.