题目描述
There are N bags of biscuits. The i-th bag contains A_i biscuits.
Takaki will select some of these bags and eat all of the biscuits inside. Here, it is also possible to select all or none of the bags.
He would like to select bags so that the total number of biscuits inside is congruent to P modulo 2. How many such ways to select bags there are?
Constraints
- $1 \leq N \leq 50$
- P = 0 or 1
- $1 \leq A_i \leq 100$
Input
Input is given from Standard Input in the following format:
N P
A_1 A_2 ... A_N
Output
Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.
Examples
Input
2 0
1 3
Output
2
Input
1 1
50
Output
0
Input
3 0
1 1 1
Output
4
Input
45 1
17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26
Output
17592186044416
输入格式
见题面
输出格式
见题面