“If you can't solve a problem, just switch to another one. What if this one is the anti-AK task?”

Given three integers $n, a, b$.

Consider all intervals $[l, r]$ such that $1 \le l < r \le n$. You need to choose some of them (possibly none), satisfying:

• All chosen intervals are contained in $[1, n]$;
• All endpoints of the chosen intervals are pairwise distinct. In other words, if the chosen intervals are $[l_1, r_1], [l_2, r_2], \dots, [l_k, r_k]$, then the $2k$ numbers $l_1, r_1, l_2, r_2, \dots, l_k, r_k$ are pairwise distinct;
• There exist $a$ chosen intervals $[l_1, r_1], [l_2, r_2], \dots, [l_a, r_a]$ such that $l_1 < l_2 < \dots < l_a$ and $r_a < r_{a-1} < \dots < r_1$;
• There exist $b$ chosen intervals $[l_1, r_1], [l_2, r_2], \dots, [l_b, r_b]$ such that $l_1 < l_2 < \dots < l_b$ and $r_1 < r_2 < \dots < r_b$.

Find the number of valid ways to choose the intervals. Since the answer may be very large, output it modulo $10^9 + 7$.

“A wise decision”

Input

The input consists of a single line containing three integers $n, a, b$ ($2 \le n \le 100$, $0 \le a, b \le n$).

Output

Output a single integer, the number of valid interval-selection schemes modulo $10^9 + 7$.

Examples

Input 1

2 0 0

Output 1

2

Input 2

2 0 1

Output 2

1

Input 3

5 1 2

Output 3

10

Input 4

9 2 3

Output 4

504

Input 5

100 14 22

Output 5

36993304