{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq K \\leq 10^9$\n*   $1 \\leq A_i \\leq 10^9$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\cdots$ $A_N$"},{"iden":"sample input 1","content":"5 4\n1 4 2 3 5"},{"iden":"sample output 1","content":"4\n\nFour sequences satisfy the condition: $(1)$, $(4,2)$, $(1,4,2)$, and $(5)$."},{"iden":"sample input 2","content":"8 4\n4 2 4 2 4 2 4 2"},{"iden":"sample output 2","content":"7\n\n$(4,2)$ is counted four times, and $(2,4)$ is counted three times."},{"iden":"sample input 3","content":"10 7\n14 15 92 65 35 89 79 32 38 46"},{"iden":"sample output 3","content":"8"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}