Powers and Modulus

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geralt

One day you and GTmac walk into a classroom and see a mysterious expression on the blackboard:

\[ (1^ b + 2^ b + \cdots + a^ b)~ \mathrm{mod}~ a \]Upon seeing the expression GTmac shows an evil smile and challenges you: “Let me give you the values of $a$ and $b$ and let’s assume $b$ is an odd number. Want to bet who can evaluate this expression? The one who loses shall buy pizza for us tonight.”

The input has two integers $a$ ($1 \leq a \leq 10^9$) and $b$ ($1\leq b\leq 99$, $b$ is odd) on a single line.

Output the value of the expression with the given $a$ and $b$.

Sample Input 1 | Sample Output 1 |
---|---|

2 3 |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

3 7 |
0 |

Sample Input 3 | Sample Output 3 |
---|---|

12345678 9 |
6172839 |