Codeforces 520E. Pluses everywhere 数学

Vasya is sitting on an extremely boring math class. To have fun, he took a piece of paper and wrote out n numbers on a single line. After that, Vasya began to write out different ways to put pluses ("+") in the line between certain digits in the line so that the result was a correct arithmetic expression; formally, no two pluses in such a partition can stand together (between any two adjacent pluses there must be at least one digit), and no plus can stand at the beginning or the end of a line. For example, in the string 100500, ways 100500 (add no pluses), 1+00+500 or 10050+0 are correct, and ways 100++500, +1+0+0+5+0+0 or 100500+ are incorrect.

The lesson was long, and Vasya has written all the correct ways to place exactly k pluses in a string of digits. At this point, he got caught having fun by a teacher and he was given the task to calculate the sum of all the resulting arithmetic expressions by the end of the lesson (when calculating the value of an expression the leading zeros should be ignored). As the answer can be large, Vasya is allowed to get only its remainder modulo 109?+?7. Help him!

Input

The first line contains two integers, n and k (0?≤?k?<?n?≤?105).

The second line contains a string consisting of n digits.

Output

Print the answer to the problem modulo 109?+?7.

Sample test(s)

input
3 1
108

output
27

input
3 2
108

output
9

Note

In the first sample the result equals (1?+?08)?+?(10?+?8)?=?27.

In the second sample the result equals 1?+?0?+?8?=?9.

/* *********************************************** Author :CKboss Created Time :2015年03月04日星期三 19时46分18秒 File Name :E.cpp ************************************************ */ #include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <string> #include <cmath> #include <cstdlib> #include <vector> #include <queue> #include <set> #include <map> using namespace std; typedef long long int LL; const LL mod = 1e9+7LL; const int maxn=100100; int n,k; LL a[maxn]; char str[maxn]; LL inv[maxn],presum[maxn]; LL jc[maxn],jcv[maxn],e[maxn]; void init() { /// inv jc e inv[1]=1; jc[0]=1; jcv[0]=1; jc[1]=1; jcv[1]=1; e[0]=1; e[1]=10; for(int i=2;i<maxn;i++) { inv[i]=inv[mod%i]*(mod-mod/i)%mod; jc[i]=(jc[i-1]*i)%mod; jcv[i]=(jcv[i-1]*inv[i])%mod; e[i]=(e[i-1]*10LL)%mod; } } LL COMB(LL n,LL m) { if(m<0||m>n) return 0LL; if(m==0||m==n) return 1LL; /// n!/((n-m)!*m!) LL ret=((jc[n]*jcv[n-m])%mod*jcv[m])%mod; return ret; } void solve(int n,int k) { LL ans=0; if(k==0) { for(int i=n-1;i>=0;i--) ans=(ans+(e[n-1-i]*a[i])%mod)%mod; cout<<ans%mod<<endl; return ; } for(int l=0;l<=n-2;l++) ans=(ans+(e[l]*COMB(n-l-2,k-1)%mod*presum[n-l-2])%mod)%mod; for(int i=0;i<=n-1;i++) ans=(ans+((a[i]*e[n-1-i])%mod*COMB(i,k))%mod)%mod; cout<<ans%mod<<endl; } int main() { //freopen("in.txt","r",stdin); //freopen("out.txt","w",stdout); init(); scanf("%d%d",&n,&k); scanf("%s",str); for(int i=0;i<n;i++) { a[i]=str[i]-'0'; if(i==0) presum[i]=a[i]; else presum[i]=(presum[i-1]+a[i])%mod; } solve(n,k); return 0; }