Sort the coins array and maintain the smallest sum that is unobtainable by induction.

If we don’t use any coins, the smallest integer that we cannot obtain by sum is <code>1</code>. Suppose currently, for a fixed set of the first several coins the smallest integer that we cannot obtain is <code>x + 1</code>, namely we can form all integers in the range <code>[1, x]</code> but not <code>x + 1</code>.

If the next unused coin’s value is NOT <code>x + 1</code> (note the array is sorted), we have to add <code>x + 1</code> to the array. After this addition, we can form all values from <code>x + 1</code> to <code>2 * x + 1</code> by adding <code>x + 1</code> in <code>[1, x]</code>'s formations. So now we can form all the numbers of <code>[1, 2 * x + 1]</code>. After this iteration the new value of <code>x</code> becomes <code>2 * x + 1</code>.