#define IOS ios_base::sync_with_stdio(0); cin.tie(0);

 #include <cstdio>//sprintf islower isupper

 #include <cstdlib>//malloc  exit strcat itoa system("cls")

 #include <iostream>//pair

 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);

 #include <bitset>

 //#include <map>

 //#include<unordered_map>

 #include <vector>

 #include <stack>

 #include <set>

 #include <string.h>//strstr substr

 #include <string>

 #include <time.h>//srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;

 #include <cmath>

 #include <deque>

 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less

 #include <vector>//emplace_back

 //#include <math.h>

 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor

 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)

 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation

 //******************

 int abss(int a);

 int lowbit(int n);

 int Del_bit_1(int n);

 int maxx(int a,int b);

 int minn(int a,int b);

 double fabss(double a);

 void swapp(int &a,int &b);

 clock_t __STRAT,__END;

 double __TOTALTIME;

 void _MS(){__STRAT=clock();}

 void _ME(){__END=clock();__TOTALTIME=(double)(__END-__STRAT)/CLOCKS_PER_SEC;cout<<"Time: "<<__TOTALTIME<<" s"<<endl;}

 //***********************

 #define rint register int

 #define fo(a,b,c) for(rint a=b;a<=c;++a)

 #define fr(a,b,c) for(rint a=b;a>=c;--a)

 #define mem(a,b) memset(a,b,sizeof(a))

 #define pr printf

 #define sc scanf

 #define ls rt<<1

 #define rs rt<<1|1

 typedef long long ll;

 const double E=2.718281828;

 const double PI=acos(-1.0);

 //const ll INF=(1LL<<60);

 const int inf=(<<);

 const double ESP=1e-;

 const int mod=(int)1e9+;

 const int N=(int)1e6+;

 int ans[N];

 void PR(int _[],int n)

 {

     for(int i=;i<=n;++i)

         pr("%d ",_[i]);

     pr("\n");

 }

 priority_queue<int>q,q3;

 int main()

 {

     int n,m;

     while(~sc("%d%d",&n,&m))

     {

         int sum=;

         while(!q.empty())q.pop();

         while(!q3.empty())q3.pop();

         for(int i=;i<=n;++i)

         {

             int tt;

             sc("%d",&tt);

             sum+=(tt+)/;

             if(tt%==)

                 q3.push(tt);

             else if(tt%==)

                 q.push(tt);

             else if(tt%==)

                 q.push(tt);

         }

         ans[]=sum;

         for(int i=;i<=m;++i)

         {

             bool f=;

             if(!q.empty())

             {

                 f=;

                 int tt=q.top();q.pop();

                 sum--;

                 if(tt->)

                 {

                     tt-=;

                     if(tt%==)

                         q3.push(tt);

                     else

                         q.push(tt);

                 }

             }

             if(!f)

             {

                 if(!q3.empty())

                 {

                     int tt=q3.top();q3.pop();

                     q.push(tt-);

                 }

             }

             ans[i]=sum;

         }

         ll ANS=;

     //    PR(ans,m);

         for(int i=;i<=m;++i)

             ANS+=ans[i],ANS%=mod;

         pr("%lld\n",ANS);

     }

     return ;

 }

 /**************************************************************************************/

 int maxx(int a,int b)

 {

     return a>b?a:b;

 }

 void swapp(int &a,int &b)

 {

     a^=b^=a^=b;

 }

 int lowbit(int n)

 {

     return n&(-n);

 }

 int Del_bit_1(int n)

 {

     return n&(n-);

 }

 int abss(int a)

 {

     return a>?a:-a;

 }

 double fabss(double a)

 {

     return a>?a:-a;

 }

 int minn(int a,int b)

 {

     return a<b?a:b;

 }