The lighting system in Binary Casino is controlled by a very complex and secure mechanism,
which is connected to a central control console. At the console, the state of each light is stored
as one bit of information ( the corresponding light is off,
light is on), so the complete state
of all lights in the building may be represented by a binary number
.
To avoid manipulation by unauthorized persons, the lighting system has a special method to
control the lights. Should one want to change the configuration of the lights, it is necessary to
enter a binary number which gets added to the original configuration
using standard integer
summation.
You need a particular number of lights to be switched ON and you are curious what are your chances of success. How many suitable binary numbers are there?
Input Specification
The first line of input contains two integers and
,
representing the number of bits of
and of
, and
the target number of lights to be switched
ON. The second line contains a binary integer
of length
.
Output Specification
Print the number of different nonnegative -bit integers
such that the sum
has exactly
bits set to 1. As the result might be large, output it modulo
.
Sample Input 1
4 2
1100
Sample Output 1
5
Sample Input 2
10 5
1000100111
Sample Output 2
260
Sample Input 3
13 1
0000000000000
Sample Output 3
13
Comments