Can I solve this problem using a Binary Search approach ?
I have already found a working mathematical solution.
Yes. Binary search should work in theory. Checking whether a specific volume can be made can be done in O(N) time and binary search is O(logN). So an O(NlogN) algorithm should pass the time limit with the given constraints. However, do check the much simpler solution given in the editorial.
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Damn I thought of that 
. But calculated the complexity wrong .
Thanks a lot .