A - Biscuits

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

いくつかのビスケットの入った袋が N 個あります．i 番目の袋には A_i 個のビスケットが入っています．

### 制約

• 1 \leq N \leq 50
• P = 0, 1
• 1 \leq A_i \leq 100

### 入力

N P
A_1 A_2 ... A_N


### 入力例 1

2 0
1 3


### 出力例 1

2


• どちらの袋も選ばない．食べるビスケットの枚数は 0 である．
• どちらの袋も選ぶ．食べるビスケットの枚数は 4 である．

### 入力例 2

1 1
50


### 出力例 2

0


### 入力例 3

3 0
1 1 1


### 出力例 3

4


### 入力例 4

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


### 出力例 4

17592186044416


Score : 200 points

### Problem Statement

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.

### Sample Input 1

2 0
1 3


### Sample Output 1

2


There are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:

• Select neither bag. The total number of biscuits is 0.
• Select both bags. The total number of biscuits is 4.

### Sample Input 2

1 1
50


### Sample Output 2

0


### Sample Input 3

3 0
1 1 1


### Sample Output 3

4


Two bags are distinguished even if they contain the same number of biscuits.

### Sample Input 4

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


### Sample Output 4

17592186044416