#include #include #include #include #include #include #include #include #include #define MAX_N 100001 #define INF_INT 2147483647 #define INF_LL 9223372036854775807 #define REP(i,n) for(int i=0;i<(int)(n);i++) using namespace std; typedef long long int ll; typedef pair P; void init(int n); int find(int n); void unite(int x,int y); bool same(int x, int y); ll bpow(ll,ll,ll); typedef vector vec; typedef vector mat; mat mul(mat &A,mat &B); mat pow(mat A,ll n); int dx[4] = {1,0,0,-1}; int dy[4] = {0,1,-1,0}; bool cmp_P(const P &a,const P &b){ return a.second < b.second; } int bitsum(ll a){ int b=0; while(a > 0){ b += a & 1; a >>= 1; } return b; } int haming(ll a,ll b){ return bitsum(a^b); } bool cmpbit(const ll a,const ll b){ return bitsum(a) < bitsum(b); } ll fact(ll n, ll MOD){ if(n==0) return 1; else return (n*fact(n-1,MOD)) % MOD; } int main() { ll N,k,res=1,MOD=10E8+7,bi=0; cin >> N >> k; bi = (1LL << N) -1; vectora(k,0); REP(i,k){ cin >> a[i]; } a.push_back(bi); a.push_back(0); sort(a.begin(),a.end(),cmpbit); if(a[0] == 0 && a[1] == 0){ a.erase(a.begin()+0); } if(a[a.size()-1] == (bi) && a[a.size()-2] == (bi)){ a.erase(a.begin()+a.size()-1); } REP(i,a.size()-1){ if(!((a[i] | a[i+1]) == a[i+1] ) || a[i] >= bi){ cout << 0 << endl; return 0; } } REP(i,a.size()-1){ res = res*((fact(haming(a[i],a[i+1]),MOD)) %MOD); res %= MOD; } cout << res << endl; return 0; } int par[MAX_N]; int ranks[MAX_N]; //n要素で初期化 void init(int n){ REP(i,n){ par[i] = i; ranks[i] = 0; } } //木の根を求める int find(int x){ if(par[x] == x){ return x; }else{ return par[x] = find(par[x]); } } void unite(int x,int y){ x = find(x); y = find(y); if(x == y) return ; if(ranks[x] < ranks[y]){ par[x] = y; }else{ par[y] = x; if(ranks[x] == ranks[y]) ranks[x]++; } } bool same(int x, int y){ return find(x) == find(y); } ll bpow(ll a, ll n,ll mod){ int i = 0; ll res=1; while(n){ if(n & 1) res = (res*a) % mod; a = (a*a) % mod; n >>= 1; } return res; } const int MOD = 1000000007; mat mul(mat &A, mat &B){ mat C(A.size(),vec(B[0].size())); REP(i,A.size())REP(k,B.size())REP(j,B[0].size()){ C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % MOD; } return C; } mat pow(mat A,ll n) { mat B(A.size(),vec(A.size())); REP(i,A.size()){ B[i][i] = 1; } while(n > 0){ if ( n & 1) B = mul(B,A); A = mul(A,A); n >>= 1; } return B; }