Lights

John has $n$ light
bulbs and a switchboard with $n$ switches; each bulb can be either
on or off, and pressing the $i$-th switch changes the state of
bulb $i$ from on to off,
and viceversa. He is using them to play a game he has made up.
In each move, John selects a (possibly empty) set of switches
and presses them, thus inverting the states of the
corresponding bulbs. After exactly $m$ moves, John would like to have the
first $v$ bulbs on and the
rest off; otherwise he loses the game. There is only one
restriction: he is not allowed to press the same *set*
of switches in two different moves.

This is quite an easy game, as there are lots of ways of winning. This has encouraged him to keep playing different winning games, and now he is intent on trying them all. Help him count how many ways of winning there are. Two games are considered the same if, after a reordering of the moves in one of them, at every step the same set of switches is pressed in both of them.

For example, if $n = 4$, $m = 3$, and $v = 2$, one possible winning game is obtained by pressing switches 1, 2 and 4 in the first move, 1 and 3 in the second one, and 1, 3 and 4 in the last one. This is considered equivalent to, say, first pressing 1 and 3; then 1, 2, 4; and then 1, 3, 4.

The input has at most 500 lines, one for each test case.
Each line contains three integers $n$ ($1
\leq n \leq 1 000$), $m$ ($1
\leq m \leq 1 000$), and $v$ ($0
\leq v \leq n$). The last line of input will hold the
values `0 0 0` and must not be
processed.

Print one line for each test case containing the number of ways John can play the game, modulo the prime $10\, 567\, 201$.

Sample Input 1 | Sample Output 1 |
---|---|

3 3 1 6 4 0 6 4 3 0 0 0 |
7 10416 9920 |