class Solution {
public:
int numWays(int n) {
if(n == 0) return 1;
if(n == 1) return 1;
if(n == 2) return 2;
int a = 1, b = 2;
for(int i = 3; i <= n; ++i) {
int tmp = (a + b) % 1000000007;
a = b;
b = tmp;
}
return b;
}
};
class Solution {
public:
int fib(int n) {
if(n == 0) return 0;
if(n == 1) return 1;
long long a = 0, b = 1;
for(int i = 2; i <= n; ++i) {
long long tmp = a + b;
tmp %= 1000000007;
a = b;
b = tmp;
}
return b;
}
};
In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 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 Fn.
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 Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).
Sample Input
0
9
999999999
1000000000
-1
Sample Output
0
34
626
6875
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:
