CF1582B Luntik and Subsequences

Luntik came out for a morning stroll and found an array $ a $ of length $ n $ . He calculated the sum $ s $ of the elements of the array ( $ s= \sum_{i=1}^{n} a_i $ ). Luntik calls a subsequence of the array $ a $ nearly full if the sum of the numbers in that subsequence is equal to $ s-1 $ . Luntik really wants to know the number of nearly full subsequences of the array $ a $ . But he needs to come home so he asks you to solve that problem! A sequence $ x $ is a subsequence of a sequence $ y $ if $ x $ can be obtained from $ y $ by deletion of several (possibly, zero or all) elements.

The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. The next $ 2 \cdot t $ lines contain descriptions of test cases. The description of each test case consists of two lines. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 60 $ ) — the length of the array. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le 10^9 $ ) — the elements of the array $ a $ .

For each test case print the number of nearly full subsequences of the array.

In the first test case, $ s=1+2+3+4+5=15 $ , only $ (2,3,4,5) $ is a nearly full subsequence among all subsequences, the sum in it is equal to $ 2+3+4+5=14=15-1 $ . In the second test case, there are no nearly full subsequences. In the third test case, $ s=1+0=1 $ , the nearly full subsequences are $ (0) $ and $ () $ (the sum of an empty subsequence is $ 0 $ ).