仅包含一个非负整数，表示 Concatenate (1 .. N) Mod M 的值。

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3
 4 #define F(i,a,b) for(int i=a;i<=b;i++)
 5 #define D(i,a,b) for(int i=a;i>=b;i--)
 6 #define ms(i,a)  memset(a,i,sizeof(a))
 7 #define LL       long long
 8 template<class T>void read(T &x){
 9     x=0; char c=getchar();
10     while (!isdigit(c)) c=getchar();
11     while (isdigit(c)) x=(x<<3)+(x<<1)+(c^48),c=getchar();
12 }
13 template<class T>void write(T x){
14     if(x>9) write(x/10);
15     putchar(48+x%10);
16 }
17
18 LL n,m,pw[20],pwm[20];
19
20 struct Matrix{
21     int x[3][3];
22     Matrix operator *(Matrix const &t)const{
23         Matrix y; ms(0,y.x);
24         F(i,0,2)F(j,0,2)F(k,0,2) y.x[i][j]=(y.x[i][j]+(LL)x[i][k]*t.x[k][j]) % m;
25         return y;
26     }
27     Matrix operator^(LL k){
28         Matrix ans,tmp;
29         ms(0,ans.x);
30         F(i,0,2) F(j,0,2) tmp.x[i][j]=x[i][j];
31         F(i,0,2) ans.x[i][i]=1;
32         while (k){
33             if(k&1) ans=ans*tmp;
34             tmp=tmp*tmp;
35             k>>=1;
36         }
37         return ans;
38     }
39 };
40
41 int main(){
42     read(n);
43     read(m);
44     int len=0;
45     LL k=n;
46     while (k){
47         len++;
48         k/=10;
49     }
50     pw[0]=1;
51     pwm[0]=1%m;
52     F(i,1,19) pw[i]=pw[i-1]*10,pwm[i]=pwm[i-1]* 10% m;
53     LL ans=0;
54     F(i,1,len-1) {
55         Matrix t;
56         ms(0,t.x);
57         t.x[0][0]=pwm[i];
58         t.x[1][0]=t.x[1][1]=1;
59         t.x[2][0]=t.x[2][1]=t.x[2][2]=1;
60         t=t^(pw[i]-pw[i-1]);
61         ans=(ans*t.x[0][0]+(pwm[i-1]-1)*t.x[1][0]+t.x[2][0])% m;
62     }
63     Matrix t;
64     ms(0,t.x);
65     t.x[0][0]=pwm[len];
66     t.x[1][0]=t.x[1][1]=1;
67     t.x[2][0]=t.x[2][1]=t.x[2][2]=1;
68     t=t^(n-pw[len-1]+1);
69     ans=(ans*t.x[0][0]+(pwm[len-1]-1)*t.x[1][0]+t.x[2][0]) % m;
70     write(ans);
71     return 0;
72 }