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"
#ifndef err
#define err(...)(void)0
#endif
using namespace std;
using ll = long long;
using ull = decltype(1ull);
template<class T>int size(T&&a) { return a.size(); }
#define REP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.first,_l##t=a.second;t<_l##t;t++)
#define RREP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.second-1,_l##t=a.first;t>=_l##t;t--)
template<class B>pair<int, B>make_pair(B b) { return{ 0,b }; }
#define rep(t,...)REP(t,make_pair(__VA_ARGS__))
#define rrep(t,...)RREP(t,make_pair(__VA_ARGS__))
#define all(a)begin(a),end(a)
#define rall(a)a.rbegin(),a.rend()
#define var(t, ...) t __VA_ARGS__;in,__VA_ARGS__;

void Calc();
int main() {
  ios::sync_with_stdio(false); cin.tie(nullptr);
  cin.exceptions(istream::failbit | istream::badbit);
  cout << fixed << setprecision(15); Calc(); cout.flush(); return 0;
}
template<class A>void amax(A&a, A b) { a = max(a, b); }
template<class A>void amin(A&a, A b) { a = min(a, b); }
template<class A>int comp(A a, A b) { return a < b ? 1 : b < a ? -1 : 0; }
struct Scanner {
  template<class A = string>A Next() { A a; cin >> a; return a; }
  template<class A = int>vector<A>Array(int n) { vector<A>a(n); for (A&i : a) cin >> i; return a; }
  string Line() const { string s; getline(cin, s); return s; }
  template<class A>Scanner&operator,(A&a) { a = Next<A>(); return *this; }
  template<class A>operator A() { return Next<A>(); }
}in;

/*---------------------------------------------------------------------*/

template<class ...T>tuple<T...>Init(T... t) { return tuple<T...>{ t... }; }
template<class T>tuple<T> Init(T t) { return tuple<T>{ t }; }
template<int N, int...I>struct idx_seq : idx_seq<N - 1, 0, (I + 1)...> {};
template<int...I>struct idx_seq<0, I...> {};
template<class R, class T, int...I>R InitInternal(T&&a, idx_seq<0, I...>) { return R{ get<I>(a)... }; }
template<class T, class B, class...V>struct Vec {
  typedef Vec<T, V...>A; typedef vector<typename A::t>t; t nvec(B a, V...b) { return t(a, A().nvec(b...)); }
};
template<class T, class B>struct Vec<T, B> {
  using X = typename conditional<is_same<T, nullptr_t>::value, int, T>::type;
  typedef vector<X>t; t nvec(B a) { return t(a); }
};
template<class T, class ...C>struct Vec<T, tuple<C...>> {
  template<class A, class B>static pair<A, B> X(A, B);
  template<class...A>static tuple<A...> X(A...);
  using t = typename conditional < is_same<T, nullptr_t>::value, decltype(X(C{}...)), T > ::type;
  t nvec(tuple<C...> a) { return InitInternal<t>(a, idx_seq<sizeof...(C)>()); }
};
template<class T, class C>struct Vec<T, tuple<C>> {
  using X = typename conditional<is_same<T, nullptr_t>::value, C, T>::type;
  using t = X; t nvec(tuple<C> a) { return { get<0>(a) }; }
};
template<class T = nullptr_t, class...B> typename Vec<T, B...>::t nvec(B...b) { return Vec<T, B...>().nvec(b...); }



void Calc() {

  var(int, n, p);

  auto a = in.Array(n);

  for (auto& i : a) {
    i = i % 2;
  }

  auto dp = nvec<ll>(n + 1, 2);
  dp[0][0] = 1;
  rep(i, n)rep(j, 2) {
    dp[i + 1][j] += dp[i][j];
    if (a[i])
      dp[i + 1][(j + 1) % 2] += dp[i][j];
    else
      dp[i + 1][j] += dp[i][j];
  }

  cout << (dp[n][p]) << endl;


}