hoj3152-Dice 等比数列求和取模

Dice
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    Source :
    Time limit : 1 sec         Memory limit : 128 M

Submitted : 82, Accepted : 18

    You have a dice with M faces, each face contains a distinct number.

    Your task is to calculate the expected number of tosses until a number facing up for consecutive N times.

    We assume when we tossing the dice, each face will occur randomly and uniformly.
Input

  Each test cases contains only one line with two integers M, N. (1<=M, N<=100000000)
Output

   For each test case, display a single line with the answer to the question above, the answer maybe very large, you need to MOD it with  1000000007.

Sample Input

5
6 1
6 2
6 3
6 4
6 5


Sample Output

1
7
43
259
1555

 1 #include<stdio.h>
 2 #define MO 1000000007
 3 long long m,n;
 4 long long powmod(long long a,long long b)
 5 {
 6     long long c=1;
 7     while(b>0)
 8     {
 9         if(b%2!=0)
10             c=c*a%MO;
11         a=a*a%MO;
12         b=b/2;
13     }
14     return c;
15 }
16 
17 long long T(long long n)
18 {
19     if(n<=1) return 1;
20     long long TN2=T(n/2);
21     if(n%2==0)
22     {
23         return (TN2 + powmod(m,n/2) * TN2)%MO;
24     }
25     else
26     {
27         return (TN2 + powmod(m,n/2) * TN2 + powmod(m,n-1))%MO;
28     }
29 }
30 
31 int main()
32 {
33     long long ans,k;
34     long long i,j,t;
35     scanf("%lld",&t);
36     for(i=1; i<=t; i++)
37     {
38         scanf("%lld%lld",&m,&n);
39         if(m==1) ans=n;
40         else
41         {
42             ans=T(n);
43         }
44         printf("%lld\n",ans);
45     }
46     return 0;
47 }