{"problem":{"name":"Rem of Sum is Num","description":{"content":"Given are a sequence of $N$ positive integers $A_1, A_2, \\ldots, A_N$, and a positive integer $K$. Find the number of non-empty contiguous subsequences in $A$ such that the remainder when dividing the","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc146_e"},"statements":[{"statement_type":"Markdown","content":"Given are a sequence of $N$ positive integers $A_1, A_2, \\ldots, A_N$, and a positive integer $K$.\nFind the number of non-empty contiguous subsequences in $A$ such that the remainder when dividing the sum of its elements by $K$ is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq K \\leq 10^9$\n*   $1 \\leq A_i \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\cdots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc146_e","tags":[],"sample_group":[["5 4\n1 4 2 3 5","4\n\nFour sequences satisfy the condition: $(1)$, $(4,2)$, $(1,4,2)$, and $(5)$."],["8 4\n4 2 4 2 4 2 4 2","7\n\n$(4,2)$ is counted four times, and $(2,4)$ is counted three times."],["10 7\n14 15 92 65 35 89 79 32 38 46","8"]],"created_at":"2026-03-03 11:01:14"}}