I've just read the Contest Analysis of this problem, and I can't figure out why the solution to the Small Case cannot work for the Large one. Imagine we check every position 30 times, and there are 1000000 (a million seems very big to me) test cases, so the probability of getting WA is at most 1 - (1 - (1 / 2 ** 30)) ** 1000000 which is less than 1e-3, which should give AC, but it doesn't. What's wrong here?
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