The symbol wedge is quite ambiguous, especially when used without context. Sometimes it is used to denote a power ( a wedge b = a^b ) and sometimes it is used to denote the XOR operation ( a wedge b=a oplus b ). You have an ambiguous expression E=A_1 wedge A_2 wedge A_3 wedge ldots wedge A_n . You can replace each wedge symbol with either a texttt{Power} operation or a texttt{XOR} operation to get an unambiguous expression E' . The value of this expression E' is determined according to the following rules: You are given an array B of length n and an integer k . The array A is given by A_i=2^{B_i} and the expression E is given by E=A_1 wedge A_2 wedge A_3 wedge ldots wedge A_n . You need to find the XOR of the values of all possible unambiguous expressions E' which can be obtained from E and has at least k wedge symbols used as texttt{XOR} operation. Since the answer can be very large, you need to find it modulo 2^{2^{20}} . Since this number can also be very large, you need to print its binary representation without leading zeroes. If the answer is equal to 0 , print 0 . The first line of input contains two integers n and k (1 <= q n <= q 2^{20}, 0 <= q k < n) . The second line of input contains n integers B_1,B_2, ldots,B_n (1 <= q B_i < 2^{20}) . Print a single line containing a binary string without leading zeroes denoting the answer to the problem. If the answer is equal to 0 , print 0 . For each of the testcases 1 to 3 , A = {2^3,2^1,2^2 } = {8,2,4 } and E=8 wedge 2 wedge 4 . For the first testcase, there is only one possible valid unambiguous expression E' = 8 oplus 2 oplus 4 = 14 = (1110)_2 . For the second testcase, there are three possible valid unambiguous expressions E' : For the third testcase, there are four possible valid unambigu