{"problem":{"name":"Shift and Decrement","description":{"content":"There are $N$ non-negative integers written on the blackboard: $A_1, ..., A_N$. Snuke can perform the following two operations at most $K$ times in total in any order: *   Operation A: Replace each i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc086_d"},"statements":[{"statement_type":"Markdown","content":"There are $N$ non-negative integers written on the blackboard: $A_1, ..., A_N$.\nSnuke can perform the following two operations at most $K$ times in total in any order:\n\n*   Operation A: Replace each integer $X$ on the blackboard with $X$ divided by $2$, rounded down to the nearest integer.\n*   Operation B: Replace each integer $X$ on the blackboard with $X$ minus $1$. This operation cannot be performed if one or more $0$s are written on the blackboard.\n\nFind the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo $1,000,000,007$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 200$\n*   $1 \\leq A_i \\leq 10^{18}$\n*   $1 \\leq K \\leq 10^{18}$\n*   $A_i$ and $K$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc086_d","tags":[],"sample_group":[["2 2\n5 7","6\n\nThere are six possible combinations of integers on the blackboard: $(1, 1)$, $(1, 2)$, $(2, 3)$, $(3, 5)$, $(4, 6)$ and $(5, 7)$. For example, $(1, 2)$ can be obtained by performing Operation A and Operation B in this order."],["3 4\n10 13 22","20"],["1 100\n10","11"],["10 123456789012345678\n228344079825412349 478465001534875275 398048921164061989 329102208281783917 779698519704384319 617456682030809556 561259383338846380 254083246422083141 458181156833851984 502254767369499613","164286011"]],"created_at":"2026-03-03 11:01:13"}}