{"problem":{"name":"O(rand)","description":{"content":"Given are $N$ pairwise distinct non-negative integers $A_1,A_2,\\ldots,A_N$. Find the number of ways to choose a set of between $1$ and $K$ numbers (inclusive) from the given numbers so that the follow","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"tokiomarine2020_e"},"statements":[{"statement_type":"Markdown","content":"Given are $N$ pairwise distinct non-negative integers $A_1,A_2,\\ldots,A_N$. Find the number of ways to choose a set of between $1$ and $K$ numbers (inclusive) from the given numbers so that the following two conditions are satisfied:\n\n*   The bitwise AND of the chosen numbers is $S$.\n*   The bitwise OR of the chosen numbers is $T$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 50$\n*   $1 \\leq K \\leq N$\n*   $0 \\leq A_i < 2^{18}$\n*   $0 \\leq S < 2^{18}$\n*   $0 \\leq T < 2^{18}$\n*   $A_i \\neq A_j$ ($1 \\leq i < j \\leq N$)\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$ $S$ $T$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"tokiomarine2020_e","tags":[],"sample_group":[["3 3 0 3\n1 2 3","2\n\nThe conditions are satisfied when we choose ${1,2}$ or ${1,2,3}$."],["5 3 1 7\n3 4 9 1 5","2"],["5 4 0 15\n3 4 9 1 5","3"]],"created_at":"2026-03-03 11:01:13"}}