Zoro is totally obsessed with the letters XYZ. Obsession here is a bit literal. He loves having space between letters X and Z.
Due to his obsession he thought of a problem:
Given integers N and K. Find the number of strings of length exactly N and having exactly K sub sequences where X and Z have exactly 1 space in between. The string can contains all upper_case English alphabets.
Note
Answer may be too large so output it modulo 109+7
Input
A single line containing N and K.
Output
Print the desired output modulo 109+7.
Constraints
1≤N≤2000
0≤K≤N
The length of the string is 3 and we need only 1 desired subsequence.
The strings can be:
XAZ ZAX
XBZ ZBX
.
.
.
.
XZZ ZZX
So there will be 54 strings possible.
