Codeforces Round 230 (Div. 1) |
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Finished |

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combinatorics

math

matrices

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C. Yet Another Number Sequence

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEveryone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation:

We'll define a new number sequence *A*_{i}(*k*) by the formula:

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).

Input

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

Output

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

Examples

Input

1 1

Output

1

Input

4 1

Output

34

Input

5 2

Output

316

Input

7 4

Output

73825

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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