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Problems > Pell Numbers Modulo

Pell Numbers Modulo

Difficulty: 1700 4000 ms 128 MB

matrix-exponentiation

The Pell sequence is P(0)=0, P(1)=1, P(n)=2P(n−1)+P(n−2). Print P(N) modulo 109+7.

Input: one integer N.

Output: the value modulo 109+7.

Constraints:

  • 1 ≤ N ≤ 1018

Sample Tests

Input 1
3
Output 1
5
Input 2
1
Output 2
1
Input 3
1000000000000000000
Output 3
3540480

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