Fibonacci

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15215		Accepted: 10687

Description

In the Fibonacci integer sequence, F₀ = 0, F₁ = 1, and F_n = F_{n − 1} + F_{n − 2} for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

An alternative formula for the Fibonacci sequence is

.

Given an integer n, your goal is to compute the last 4 digits of F_n.

Input

The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.

Output

For each test case, print the last four digits of F_n. If the last four digits of F_n are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print F_n mod 10000).

Sample Input

099999999991000000000-1

Sample Output

0346266875

Hint

As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by

.

Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:

.

Source

 

1 #include
      
        2 #include
       
         3 #include
        
          4 #include
         
           5 using namespace std; 6 int n,a[2][2],b[2][2]; 7 void mul(int a[2][2],int b[2][2],int ans[2][2]){ 8     int t[2][2]; 9     for(int i=0;i<2;i++)10         for(int j=0;j<2;j++){11             t[i][j]=0;12             for(int k=0;k<2;k++) t[i][j]=(t[i][j]+a[i][k]*b[k][j])%10000; 13         }14     for(int i=0;i<2;i++)15         for(int j=0;j<2;j++) ans[i][j]=t[i][j];16 } 17 int main(){18     while(scanf("%d",&n)){19         if(n==-1) return 0;20         a[0][0]=a[1][0]=a[0][1]=b[0][0]=b[1][1]=1;21         a[1][1]=b[1][0]=b[0][1]=0;22         while(n){23             if(n&1) mul(a,b,b);24             n>>=1;25             mul(a,a,a);26         }27         printf("%d\n",b[1][0]);28     }29     return 0;30 }