Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#pragma GCC target("avx")
//#pragma GCC target("avx512f,avx512dq,avx512cd,avx512bw,avx512vl")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define DB double
#define LD long double
#define ST string
#define BS bitset
#define PA pair<LL,LL>
#define VE vector
#define VL vector<LL>
#define VP vector<pair<LL,LL>>
#define VVL vector<vector<LL>>
#define PQ priority_queue
#define PQS priority_queue<LL,vector<LL>,greater<LL>>
#define FI first
#define SE second
#define PB push_back
#define POB pop_back
#define PF push_front
#define POF pop_front
#define EB emplace_back
#define MP make_pair
#define TS to_string
#define TU to_ullong
#define BPL __builtin_popcountll
#define FOR(i,a,n) for(i=a;i<n;++i)
#define FORR(i,a,n) for(i=n-1;i>=a;--i)
#define rep(i,n) FOR(i,0,n)
#define repr(i,n) FORR(i,0,n)
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define SORT(a) sort(ALL(a))
#define REV(a) reverse(ALL(a))
#define UB(a,n) *upper_bound(ALL(a),n)
#define UBn(a,n) upper_bound(ALL(a),n)-a.begin()
#define LB(a,n) *lower_bound(ALL(a),n)
#define LBn(a,n) lower_bound(ALL(a),n)-a.begin()
#define INF 1145141919810364364LL
#define PI 3.14159265358979
#define MOD 1000000007
//#define MOD 998244353
#define ERR 0.00000001
#define FAST cin.tie(0);ios::sync_with_stdio(false)

void Yn(LL a){if(a)printf("Yes\n");else printf("No\n");}
void YN(LL a){if(a)printf("YES\n");else printf("NO\n");}
LL pwmn(LL a,LL n){LL ans=1;while(ans<a)ans*=n;return ans;}
LL dig(LL n){LL ret=0;while(n)n/=10,ret++;return ret;}
LL GCD(LL a,LL b){LL c=1,tmp=max(a,b);b=min(a,b);a=tmp;while(c!=0){c=a%b;a=b;b=c;}return a;}
LL LCM(LL a,LL b){return a*b/GCD(a,b);}
int lcmp(const void* a,const void* b){if(*(LL*)a>*(LL*)b)return 1;if(*(LL*)a<*(LL*)b)return -1;return 0;}
int lcmpr(const void* a,const void* b){if(*(LL*)a>*(LL*)b)return -1;if(*(LL*)a<*(LL*)b)return 1;return 0;}
int ccmp(const void* a,const void* b){return *(char*)a-*(char*)b;}
int ccmpr(const void* a,const void* b){return *(char*)b-*(char*)a;}
int scmp(const void* a,const void* b){return strcmp((char*)a,(char*)b);}
int scmpr(const void* a,const void* b){return strcmp((char*)b,(char*)a);}
LL cmod(LL a,LL m){if(a%m<0)return a%m+abs(m);else return a%m;}
LL DIV(LL a,LL d,LL m){LL l=m,x=1,y=0,k;while(l){k=d/l;d-=k*l;swap(l,d);x-=k*y;swap(x,y);}return cmod(a*cmod(x,m),m);}
LL POW(LL a,LL n,LL m){LL ans=1;while(n>0){if(n&1)ans=ans*a%m;a=a*a%m;n>>=1;}return ans;}
VL fact,finv,inv;
void comi(LL n){LL i;fact.resize(max(2LL,n+1));finv.resize(max(2LL,n+1));inv.resize(max(2LL,n+1));fact[0]=fact[1]=1;finv[0]=finv[1]=1;inv[1]=1;FOR(i,2,n+1){fact[i]=fact[i-1]*i%MOD;inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;finv[i]=finv[i-1]*inv[i]%MOD;}}
LL com(LL n,LL k){if(n<k||n<0||k<0)return 0;return fact[n]*(finv[k]*finv[n-k]%MOD)%MOD;}
bool cmps(pair<LL,LL> a,pair<LL,LL> b){if(a.second!=b.second)return a.second<b.second;return a.first<b.first;}
template<typename T>bool chmax(T &a,T b){if(a<b){a=b;return true;}return false;}
template<typename T>bool chmin(T &a,T b){if(a>b){a=b;return true;}return false;}

#define MI modint<MOD>
template<int mod>struct modint{
	int x;
	modint():x(0){}
	modint(LL n):x(n>=0?n%mod:(mod-(-n)%mod)%mod){}
	modint &operator+=(const modint &n){if((x+=n.x)>=mod)x-=mod;return *this;}
	modint &operator-=(const modint &n){if((x+=mod-n.x)>=mod)x-=mod;return *this;}
	modint &operator++(){*this+=1;return *this;}
  modint &operator--(){*this-=1;return *this;}
	modint &operator*=(const modint &n){x=(int)((LL)x*n.x%mod);return *this;}
	modint &operator/=(const modint &n){*this*=n.inv();return *this;}
	modint operator-()const{return modint(-x);}
	modint operator+(const modint &n)const{return modint(*this)+=n;}
	modint operator-(const modint &n)const{return modint(*this)-=n;}
	modint operator++(int){modint ret(*this);*this+=1;return ret;}
  modint operator--(int){modint ret(*this);*this-=1;return ret;}
	modint operator*(const modint &n)const{return modint(*this)*=n;}
	modint operator/(const modint &n)const{return modint(*this)/=n;}
	bool operator<(const modint &n)const{return x<n.x;}
	bool operator>(const modint &n)const{return x>n.x;}
	bool operator<=(const modint &n)const{return x<=n.x;}
	bool operator>=(const modint &n)const{return x>=n.x;}
	bool operator!=(const modint &n)const{return x!=n.x;}
	bool operator==(const modint &n)const{return x==n.x;}
	friend istream &operator>>(istream &is,modint &n){LL l;is>>l;n=modint<mod>(l);return is;}
	friend ostream &operator<<(ostream &os,const modint &n){return os<<n.x;}
	int getmod(){return mod;}
	modint inv()const{int a=x,b=mod,c=1,d=0,n;while(b){n=a/b;swap(a-=n*b,b);swap(c-=n*d,d);}return modint(c);}
	modint pow(LL n)const{modint ret(1),m(x);while(n){if(n&1)ret*=m;m*=m;n>>=1;}return ret;}
};

int main(){
  FAST;
  LL i,N,K,f=0,Z=0,m=0,p=0;
	MI ans=1;
	LD a=0,b=0;
	cin>>N>>K;
	VP V(N);
	VL P,M;
	rep(i,N){
		cin>>V[i].FI;
		if(V[i].FI<0)V[i].FI=-V[i].FI,V[i].SE=1,M.PB(V[i].FI);
		else if(V[i].FI==0)++Z;
		else P.PB(V[i].FI);
	}
	SORT(V);
	REV(V);
	SORT(P);
	REV(P);
	SORT(M);
	REV(M);
	rep(i,K){
		ans*=V[i].FI,f^=V[i].SE;
		if(V[i].SE)++m;
		else ++p;
		if(!V[i].FI){
			cout<<0<<endl;
			return 0;
		}
	}
	if(f){
		if(!P.size()){
			REV(M);
			ans=1;
			rep(i,K)ans*=M[i];
			ans*=-1;
			if(Z)ans=0;
			cout<<ans<<endl;
			return 0;
		}
		if(m==M.size()&&p==P.size()){
			ans*=-1;
			if(Z)ans=0;
			cout<<ans<<endl;
			return 0;
		}
		if(p==P.size()){
			cout<<ans*M[m]/P[p-1]<<endl;
			return 0;
		}
		if(m==M.size()){
			cout<<ans*P[p]/M[m-1]<<endl;
			return 0;
		}
		a=(LD)M[m]/P[p-1];
		b=(LD)P[p]/M[m-1];
		if(a<b)ans=ans*M[m]/P[p-1];
		else ans=ans*P[p]/M[m-1];
	}
	cout<<ans<<endl;
}