The numbers 1,2,…,2013 are written on 2013 stones weighing 1,2,…,2013 grams such that each number is used exactly once. We have a two-pan balance that shows the difference between the weights at the left and the right pans. No matter how the numbers are written, if it is possible to determine in k weighings whether the weight of each stone is equal to the number that is written on the stone, what is the least possible value of k?<spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> None of above combinatorics proposedcombinatorics