运

【问题背景】
zhx 和妹子们玩数数游戏。

 

【问题描述】

仅包含4或7的数被称为幸运数。一个序列的子序列被定义为从序列中删去若干个数， 剩下的数组成的新序列。两个子序列被定义为不同的当且仅当其中的元素在原始序列中的下标的集合不相等。对于一个长度为 N的序列，共有 2^N个不同的子序列。（ 包含一个空序列）。一个子序列被称为不幸运的， 当且仅当其中不包含两个或两个以上相同的幸运数。对于一个给定序列，求其中长度恰好为 K 的不幸运子序列的个数， 答案mod 10^9+7 输出。

 

【输入格式】

第一行两个正整数 N， K， 表示原始序列的长度和题目中的 K。

接下来一行 N 个整数 ai， 表示序列中第 i 个元素的值。

 

【输出格式】

仅一个数，表示不幸运子序列的个数。（ mod 10^9+7）

 

【样例输入】
3 2
1 1 1
【样例输出】
3

【样例输入】
4 2
4 7 4 7
【样例输出】
4

 

【样例解释】
对于样例 1，每个长度为 2 的子序列都是符合条件的。

对于样例 2，4个不幸运子序列元素下标分别为：{1, 2}, {3, 4}, {1, 4}, {2, 3}。注意下标集{1, 3}对应的子序列不是“不幸运”的， 因为它包含两个相同的幸运数4.

【数据规模与约定】
对于50%的数据， 1 ≤N ≤ 16。

对于70%的数据， 1 ≤ N ≤ 1000, ai ≤ 10000。

对于100%的数据， 1 ≤ N ≤ 100000,K ≤ N, 1 ≤ ai ≤10^9。

 

【题解】

      考试的时候完全读错了题，直接当做字符串生成子序列来做，对整个题目的理解非常不到位。退一步说，就算注意到这不是个字符串的题，对乘法逆元的理解也很不到位，更不要说打出来了。一般来说，除了数学题之外的题起码还能走到正解附近，数学题就是完全不知道正解是什么啊……

       正解是打表处理幸运数字，用map处理出每个幸运数字出现的次数。在不幸运序列里每个幸运数字只可能出现0次或1次，所以幸运数字对答案的贡献可以用dp来解决。设dp[i][j]表示从前i个幸运数字中选j个的方案数，则dp方程为：

      dp[i][j] = dp[i − 1][j] + dp[i − 1][j − 1] ∗ C[i]

      c[i]是刚才用map处理出的幸运数字i在原序列中出现次数，dp[i][0]均初始化为1。设共出现了tot种幸运数字，非幸运数个数为d，则结果为：

      sigmaC(d,k-i)*dp[tot][i]  1<=i<=min(tot,k)

       这里的组合数非常大了，不能递推，又需要准确值，根据C(n,k)=n!/(n-k)!k!，预处理出足够大的阶乘，再求分母上阶乘关于10^9+7的逆元计算即可。数非常大，需要每一次都取模才能阻止溢出。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#define ll long long
using namespace std;
int n,k,a[100010];
int lu[1100]={4,7,44,47,74,77,444,447,474,477,744,747,774,777,4444,4447,4474,4477,4744,4747,4774,4777,7444,7447,7474,7477,7744,7747,7774,7777,44444,44447,44474,44477,44744,44747,44774,44777,47444,47447,47474,47477,47744,47747,47774,47777,74444,74447,74474,74477,74744,74747,74774,74777,77444,77447,77474,77477,77744,77747,77774,77777,444444,444447,444474,444477,444744,444747,444774,444777,447444,447447,447474,447477,447744,447747,447774,447777,474444,474447,474474,474477,474744,474747,474774,474777,477444,477447,477474,477477,477744,477747,477774,477777,744444,744447,744474,744477,744744,744747,744774,744777,747444,747447,747474,747477,747744,747747,747774,747777,774444,774447,774474,774477,774744,774747,774774,774777,777444,777447,777474,777477,777744,777747,777774,777777,4444444,4444447,4444474,4444477,4444744,4444747,4444774,4444777,4447444,4447447,4447474,4447477,4447744,4447747,4447774,4447777,4474444,4474447,4474474,4474477,4474744,4474747,4474774,4474777,4477444,4477447,4477474,4477477,4477744,4477747,4477774,4477777,4744444,4744447,4744474,4744477,4744744,4744747,4744774,4744777,4747444,4747447,4747474,4747477,4747744,4747747,4747774,4747777,4774444,4774447,4774474,4774477,4774744,4774747,4774774,4774777,4777444,4777447,4777474,4777477,4777744,4777747,4777774,4777777,7444444,7444447,7444474,7444477,7444744,7444747,7444774,7444777,7447444,7447447,7447474,7447477,7447744,7447747,7447774,7447777,7474444,7474447,7474474,7474477,7474744,7474747,7474774,7474777,7477444,7477447,7477474,7477477,7477744,7477747,7477774,7477777,7744444,7744447,7744474,7744477,7744744,7744747,7744774,7744777,7747444,7747447,7747474,7747477,7747744,7747747,7747774,7747777,7774444,7774447,7774474,7774477,7774744,7774747,7774774,7774777,7777444,7777447,7777474,7777477,7777744,7777747,7777774,7777777,44444444,44444447,44444474,44444477,44444744,44444747,44444774,44444777,44447444,44447447,44447474,44447477,44447744,44447747,44447774,44447777,44474444,44474447,44474474,44474477,44474744,44474747,44474774,44474777,44477444,44477447,44477474,44477477,44477744,44477747,44477774,44477777,44744444,44744447,44744474,44744477,44744744,44744747,44744774,44744777,44747444,44747447,44747474,44747477,44747744,44747747,44747774,44747777,44774444,44774447,44774474,44774477,44774744,44774747,44774774,44774777,44777444,44777447,44777474,44777477,44777744,44777747,44777774,44777777,47444444,47444447,47444474,47444477,47444744,47444747,47444774,47444777,47447444,47447447,47447474,47447477,47447744,47447747,47447774,47447777,47474444,47474447,47474474,47474477,47474744,47474747,47474774,47474777,47477444,47477447,47477474,47477477,47477744,47477747,47477774,47477777,47744444,47744447,47744474,47744477,47744744,47744747,47744774,47744777,47747444,47747447,47747474,47747477,47747744,47747747,47747774,47747777,47774444,47774447,47774474,47774477,47774744,47774747,47774774,47774777,47777444,47777447,47777474,47777477,47777744,47777747,47777774,47777777,74444444,74444447,74444474,74444477,74444744,74444747,74444774,74444777,74447444,74447447,74447474,74447477,74447744,74447747,74447774,74447777,74474444,74474447,74474474,74474477,74474744,74474747,74474774,74474777,74477444,74477447,74477474,74477477,74477744,74477747,74477774,74477777,74744444,74744447,74744474,74744477,74744744,74744747,74744774,74744777,74747444,74747447,74747474,74747477,74747744,74747747,74747774,74747777,74774444,74774447,74774474,74774477,74774744,74774747,74774774,74774777,74777444,74777447,74777474,74777477,74777744,74777747,74777774,74777777,77444444,77444447,77444474,77444477,77444744,77444747,77444774,77444777,77447444,77447447,77447474,77447477,77447744,77447747,77447774,77447777,77474444,77474447,77474474,77474477,77474744,77474747,77474774,77474777,77477444,77477447,77477474,77477477,77477744,77477747,77477774,77477777,77744444,77744447,77744474,77744477,77744744,77744747,77744774,77744777,77747444,77747447,77747474,77747477,77747744,77747747,77747774,77747777,77774444,77774447,77774474,77774477,77774744,77774747,77774774,77774777,77777444,77777447,77777474,77777477,77777744,77777747,77777774,77777777,444444444,444444447,444444474,444444477,444444744,444444747,444444774,444444777,444447444,444447447,444447474,444447477,444447744,444447747,444447774,444447777,444474444,444474447,444474474,444474477,444474744,444474747,444474774,444474777,444477444,444477447,444477474,444477477,444477744,444477747,444477774,444477777,444744444,444744447,444744474,444744477,444744744,444744747,444744774,444744777,444747444,444747447,444747474,444747477,444747744,444747747,444747774,444747777,444774444,444774447,444774474,444774477,444774744,444774747,444774774,444774777,444777444,444777447,444777474,444777477,444777744,444777747,444777774,444777777,447444444,447444447,447444474,447444477,447444744,447444747,447444774,447444777,447447444,447447447,447447474,447447477,447447744,447447747,447447774,447447777,447474444,447474447,447474474,447474477,447474744,447474747,447474774,447474777,447477444,447477447,447477474,447477477,447477744,447477747,447477774,447477777,447744444,447744447,447744474,447744477,447744744,447744747,447744774,447744777,447747444,447747447,447747474,447747477,447747744,447747747,447747774,447747777,447774444,447774447,447774474,447774477,447774744,447774747,447774774,447774777,447777444,447777447,447777474,447777477,447777744,447777747,447777774,447777777,474444444,474444447,474444474,474444477,474444744,474444747,474444774,474444777,474447444,474447447,474447474,474447477,474447744,474447747,474447774,474447777,474474444,474474447,474474474,474474477,474474744,474474747,474474774,474474777,474477444,474477447,474477474,474477477,474477744,474477747,474477774,474477777,474744444,474744447,474744474,474744477,474744744,474744747,474744774,474744777,474747444,474747447,474747474,474747477,474747744,474747747,474747774,474747777,474774444,474774447,474774474,474774477,474774744,474774747,474774774,474774777,474777444,474777447,474777474,474777477,474777744,474777747,474777774,474777777,477444444,477444447,477444474,477444477,477444744,477444747,477444774,477444777,477447444,477447447,477447474,477447477,477447744,477447747,477447774,477447777,477474444,477474447,477474474,477474477,477474744,477474747,477474774,477474777,477477444,477477447,477477474,477477477,477477744,477477747,477477774,477477777,477744444,477744447,477744474,477744477,477744744,477744747,477744774,477744777,477747444,477747447,477747474,477747477,477747744,477747747,477747774,477747777,477774444,477774447,477774474,477774477,477774744,477774747,477774774,477774777,477777444,477777447,477777474,477777477,477777744,477777747,477777774,477777777,744444444,744444447,744444474,744444477,744444744,744444747,744444774,744444777,744447444,744447447,744447474,744447477,744447744,744447747,744447774,744447777,744474444,744474447,744474474,744474477,744474744,744474747,744474774,744474777,744477444,744477447,744477474,744477477,744477744,744477747,744477774,744477777,744744444,744744447,744744474,744744477,744744744,744744747,744744774,744744777,744747444,744747447,744747474,744747477,744747744,744747747,744747774,744747777,744774444,744774447,744774474,744774477,744774744,744774747,744774774,744774777,744777444,744777447,744777474,744777477,744777744,744777747,744777774,744777777,747444444,747444447,747444474,747444477,747444744,747444747,747444774,747444777,747447444,747447447,747447474,747447477,747447744,747447747,747447774,747447777,747474444,747474447,747474474,747474477,747474744,747474747,747474774,747474777,747477444,747477447,747477474,747477477,747477744,747477747,747477774,747477777,747744444,747744447,747744474,747744477,747744744,747744747,747744774,747744777,747747444,747747447,747747474,747747477,747747744,747747747,747747774,747747777,747774444,747774447,747774474,747774477,747774744,747774747,747774774,747774777,747777444,747777447,747777474,747777477,747777744,747777747,747777774,747777777,774444444,774444447,774444474,774444477,774444744,774444747,774444774,774444777,774447444,774447447,774447474,774447477,774447744,774447747,774447774,774447777,774474444,774474447,774474474,774474477,774474744,774474747,774474774,774474777,774477444,774477447,774477474,774477477,774477744,774477747,774477774,774477777,774744444,774744447,774744474,774744477,774744744,774744747,774744774,774744777,774747444,774747447,774747474,774747477,774747744,774747747,774747774,774747777,774774444,774774447,774774474,774774477,774774744,774774747,774774774,774774777,774777444,774777447,774777474,774777477,774777744,774777747,774777774,774777777,777444444,777444447,777444474,777444477,777444744,777444747,777444774,777444777,777447444,777447447,777447474,777447477,777447744,777447747,777447774,777447777,777474444,777474447,777474474,777474477,777474744,777474747,777474774,777474777,777477444,777477447,777477474,777477477,777477744,777477747,777477774,777477777,777744444,777744447,777744474,777744477,777744744,777744747,777744774,777744777,777747444,777747447,777747474,777747477,777747744,777747747,777747774,777747777,777774444,777774447,777774474,777774477,777774744,777774747,777774774,777774777,777777444,777777447,777777474,777777477,777777744,777777747,777777774,777777777};
map<int,int> ma;
int ck[1100],ge,d;
ll ans,mod=1000000007,f[1100][1100],jc[100010];
ll e_gcd(ll n,ll m,ll &x,ll &y)
{
     if(m==0)
     {
        x=1;
        y=0;
        return n;
     }
     ll an=e_gcd(m,n%m,x,y);
     ll t=x;
     x=y;
     y=t-n/m*y;
     return an;
}
ll ny(ll n,ll m)
{
     ll x,y;
     ll gcd=e_gcd(n,m,x,y);
     x*=1/gcd;
     m=abs(m);
     ll jg=x%m;
     if(jg<=0)
       jg+=m;
     return jg;
}
void dp()
{
     for(int i=0;i<=ge;i++) f[i][0]=1;
     for(int i=1;i<=ge;i++)
       for(int j=1;j<=i;j++)
         f[i][j]=(f[i-1][j]+f[i-1][j-1]*ck[i])%mod;
}
int main()
{
    scanf("%d%d",&n,&k);
    for(int i=0;i<1022;i++)
        ma[lu[i]]=0;
    for(int i=1;i<=n;i++)
    {
       scanf("%d",&a[i]);
       if(ma.count(a[i]))
         ma[a[i]]=ma[a[i]]+1;
    }
    d=n;
    for(int i=0;i<1022;i++)
      if(ma[lu[i]]!=0)
      {
        ge++;
        ck[ge]=ma[lu[i]];
        d-=ck[ge];
      }
    jc[0]=jc[1]=1;
    dp();
    for(int i=2;i<=d;i++)
      jc[i]=(i*jc[i-1])%mod;
    for(int i=0;i<=ge&&i<=k;i++)
      ans=(ans+((jc[d]*ny(jc[d-k+i],mod))%mod*ny(jc[k-i],mod)%mod)*f[ge][i])%mod;
    printf("%lld",ans%mod);
    return 0;
}