Sereja is interested in intervals of numbers, so he has prepared a problem about intervals for you. An interval of numbers is a pair of integers $[*l*, *r*]$ $(1 ≤ *l* ≤ *r* ≤ *m*)$. Interval $[*l*_{1}, *r*_{1}]$ belongs to interval $[*l*_{2}, *r*_{2}]$ if the following condition is met: $*l*_{2} ≤ *l*_{1} ≤ *r*_{1} ≤ *r*_{2}$.

Sereja wants to write out a sequence of $*n*$ intervals $[*l*_{1}, *r*_{1}]$, $[*l*_{2}, *r*_{2}]$, $...$, $[*l*_{*n*}, *r*_{*n*}]$ on a piece of paper. At that, no interval in the sequence can belong to some other interval of the sequence. Also, Sereja loves number $*x*$ very much and he wants some (at least one) interval in the sequence to have $*l*_{*i*} = *x*$. Sereja wonders, how many distinct ways to write such intervals are there?

Help Sereja and find the required number of ways modulo $1000000007$ $(10^{9} + 7)$.

Two ways are considered distinct if there is such $*j*$ $(1 ≤ *j* ≤ *n*)$, that the $*j*$-th intervals in two corresponding sequences are not equal.

Input

The first line contains integers $*n*$, $*m*$, $*x*$ $(1 ≤ *n*·*m* ≤ 100000, 1 ≤ *x* ≤ *m*)$ — the number of segments in the sequence, the constraints on the numbers in segments and Sereja's favourite number.

Output

In a single line print the answer modulo $1000000007$ $(10^{9} + 7)$.

Note

In third example next sequences will be correct: ${[1, 1], [3, 3]}$, ${[1, 2], [3, 3]}$, ${[2, 2], [3, 3]}$, ${[3, 3], [1, 1]}$, ${[3, 3], [2, 2]}$, ${[3, 3], [1, 2]}$.