In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1,2,3,⋯,n} is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry.
Calculate the number of the alternating permutations p1,p2,⋯,pn such that p1=a and pn=b.
Input
The first line of the input contains three integers n, a and b.
It is guaranteed that 2≤n≤2000 and 1≤a,b≤n and a≠b.
Output
Output a single line contains a single integer, indicating the answer.
Example
Input
2000 249 662
Output
979748465