B"This is an interactive problem. Note: the XOR-sum of an array a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^9 ) is defined as a_1 oplus a_2 oplus ldots oplus a_n , where oplus denotes the bitwise XOR operation. Little Dormi received an array of n integers a_1, a_2, ldots, a_n for Christmas. However, while playing with it over the winter break, he accidentally dropped it into his XOR machine, and the array got lost. The XOR machine is currently configured with a query size of k (which you cannot change), and allows you to perform the following type of query: by giving the machine k distinct indices x_1, x_2, ldots, x_k , it will output a_{x_1} oplus a_{x_2} oplus ldots oplus a_{x_k} . As Little Dormi's older brother, you would like to help him recover the XOR-sum of his array a_1, a_2, ldots, a_n by querying the XOR machine. Little Dormi isn't very patient, so to be as fast as possible, you must query the XOR machine the minimum number of times to find the XOR-sum of his array. Formally, let d be the minimum number of queries needed to find the XOR-sum of any array of length n with a query size of k . Your program will be accepted if you find the correct XOR-sum in at most d queries. Lastly, you also noticed that with certain configurations of the machine k and values of n , it may not be possible to recover the XOR-sum of Little Dormi's lost array. If that is the case, you should report it as well. The array a_1, a_2, ldots, a_n is fixed before you start querying the XOR machine and does not change with the queries. The only line of input contains the integers n and k ( 1 <= n <= 500 , 1 <= k <= n ), the length of the lost array and the configured query size of the XOR machine. Elements of the original array satisfy 1 <= a_i <= 10^9 . It can be proven that that if it is possible to recover the XOR sum under the given "...