P130.cpp

#include <iostream>

int main() {
  int men[100];
  while(true) {
    int n, k;
    std::cin >> n >> k;
    if(n == 0)
      return 0;
    // set up:
    int maxI = n-1;
    int i = maxI;
    for(int j = 0; j < n; ++j) {
      men[j] = j+1;
    }
    // calculate:
    while(maxI > 0) {
      /*
      for(int j = 0; j <= maxI; ++j) {
	std::cerr << " ";
	if(j == i) 
	  std::cerr << "(";
	std::cerr << men[j];
	if(j == i) 
	  std::cerr << ")";
      }
      std::cerr << std::endl;//*/
      // Kill:
      int toDieI = (i + k)%(1+maxI);
      // Walk to replacement:
      int toReplaceI = (toDieI+1)%(1+maxI);
      for(int j = 1; j < k; ++j) {
	toReplaceI = (toReplaceI+1)%(1+maxI);
	if(toReplaceI == toDieI)
	  toReplaceI = (toReplaceI+1)%(1+maxI);
      }
      //std::cerr << "Killing " << men[toDieI] << "@" << toDieI << " -> " << men[toReplaceI] << "@" << toReplaceI << std::endl;
      // Replace dead guy:
      men[toDieI] = men[toReplaceI];
      // Shuffle all down:
      for(int j = toReplaceI; j < maxI; ++j) {
	men[j] = men[j+1];
      }
      --maxI;
      // update i:
      i = toDieI;
      if(toDieI > toReplaceI)
	--i;
    }
    // output:
    std::cout << ((n+1-men[0])%n+1) << std::endl;
  }
}