{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence $A=(A_0,A_1,\\ldots,A_{N-1})$ of length $N$.  \nThere is an initially empty dish. Takahashi is going to repeat the following operation $K$ times.\n\n*   Let $X$ be the number of candies on the dish. He puts $A_{(X\\bmod N)}$ more candies on the dish. Here, $X\\bmod N$ denotes the remainder when $X$ is divided by $N$.\n\nFind how many candies are on the dish after the $K$ operations."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq K \\leq 10^{12}$\n*   $1 \\leq A_i\\leq 10^6$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_0$ $A_1$ $\\ldots$ $A_{N-1}$"},{"iden":"sample input 1","content":"5 3\n2 1 6 3 1"},{"iden":"sample output 1","content":"11\n\nThe number of candies on the dish transitions as follows.\n\n*   In the $1$\\-st operation, we have $X=0$, so $A_{(0\\mod 5)}=A_0=2$ more candies will be put on the dish.\n*   In the $2$\\-nd operation, we have $X=2$, so $A_{(2\\mod 5)}=A_2=6$ more candies will be put on the dish.\n*   In the $3$\\-rd operation, we have $X=8$, so $A_{(8\\mod 5)}=A_3=3$ more candies will be put on the dish.\n\nThus, after the $3$ operations, there will be $11$ candies on the dish. Note that you must **not** print the remainder divided by $N$."},{"iden":"sample input 2","content":"10 1000000000000\n260522 914575 436426 979445 648772 690081 933447 190629 703497 47202"},{"iden":"sample output 2","content":"826617499998784056\n\nThe answer may not fit into a $32$\\-bit integer type."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}