Problem:
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

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define REP(i, n) for(int i = 0;i < n;i++)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end())
#define VRSORT(v) sort(v.rbegin(), v.rend())
#define ll long long
#define pb(a) push_back(a)
#define MOD 1000000007
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

typedef vector<unsigned int>vec;
typedef vector<vec> mat;
//typedef tuple<ll, ll, ll> T;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

void add(ll& a, ll b){a = (a+b) % MOD;}

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

const int INF = 1e9;
const ll LINF = 1e18;
const ll NMAX = 1e2;
ll fac[NMAX + 1], inv[NMAX + 1], finv[NMAX + 1];

ll mod_pow(ll base, ll index, ll mod) {
    if(index == 0) return 1LL;
    ll res = mod_pow((base * base) % mod, index / 2, mod);
    if(index & 1) (res *= base) %= mod;
    return res;
}

void cominit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for(int i=2;i<NMAX + 1;i++) {
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
 
ll comb(ll n, ll k) {
    if(n < k) return 0;
    if(n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,p;
    cin>>N>>p;
    vector<ll> A(N);
    cominit();
    int odd=0,even=0;
    REP(i,N){
        cin>>A[i];
        if(A[i]%2) odd++;
        else even++;
    }
    ll ans=0;
    if(p){
        for(int i=0;2*i+1<=odd;i++) ans+=comb(odd,2*i+1);
        ans*=mod_pow(2LL,even,LINF);
    }
    else{
        for(int i=0;2*i<=odd;i++) ans+=comb(odd,2*i);
        ans*=mod_pow(2LL,even,LINF);
    }
    cout<<ans<<endl;
}