Problems
Just Add It
Just Add It
For two given integers $n$ and $k$ find
$$
(Z_n + Z_{n-1} - 2 \cdot Z_{n-2})~mod~10000007,
$$
where
$$
Z_n = S_n + P_n,
$$
$$
S_n = 1^k + 2^k + 3^k + ... + n^k,
$$
$$
P_n = 1^1 + 2^2 + 3^3 + ... + n^n
$$
\InputFile
There are several test cases. Each case is a separate line that contains two positive integers $n$ and $k~(1 < n < 2 \cdot 10^8, 0 < k < 10^6)$. The last line contains two zeros and should not be processed.
\OutputFile
For each test case print the required value in a separate line.
Input example #1
10 3 9 31 83 17 5 2 0 0
Output example #1
4835897 2118762 2285275 3694