Description
Uncle Huang wants to find a tutor. He has n students to choose from.
Students are indexed 1, 2, . . . , n and standing in a circle.
Uncle Huang will count every k-th students in clock-wise.
The k-th student is going to be chosen but the student will disappear(Nobody knows why!) therefore Uncle Huang will continue his counting and start from the next student.
The last remaining student will be his tutor.
Tell Uncle Huang the index of the student who will be his tutor.
example: If n = 5, k = 7
Hint: 約瑟夫斯問題(https://zh.wikipedia.org/wiki/%E7%BA%A6%E7%91%9F%E5%A4%AB%E6%96%AF%E9%97%AE%E9%A2%98)
This problem is partial judge.
Note: k might be very large, if you just count k students you will get TLE. Try to count less by using mod.
Input
The input will end by EOF
Every testcase only contains two integer n(1<= n <= 1000) and k(1 <= k <= 109)
Output
For each testcase print the index of the student who last remaining.
remember to print \n at the end of every output.