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A9275 | $Yet Another Number Sequence$

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内存限制256MB

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题目描述

Everyone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation: $F_{1}=1,F_{2}=2,F_{i}=F_{i-1}+F_{i-2} (i>2).$ We'll define a new number sequence $A_{i}(k)$ by the formula: $A_{i}(k)=F_{i}×i^{k} (i>=1).$ In this problem, your task is to calculate the following sum: $A_{1}(k)+A_{2}(k)+...+A_{n}(k)$ . The answer can be very large, so print it modulo $1000000007$ $(10^{9}+7)$ .

输入格式

The first line contains two space-separated integers $n$ , $k$ $(1<=n<=10^{17}; 1<=k<=40)$ .

输出格式

Print a single integer — the sum of the first $n$ elements of the sequence $A_{i}(k)$ modulo $1000000007$ $(10^{9}+7)$ .

输入输出样例

输入 #1

1 1

输出 #1

输入 #2

4 1

输出 #2

输入 #3

5 2

输出 #3

输入 #4

7 4

输出 #4

C++ 编辑器

输入

输出