{"raw_statement":[{"iden":"problem statement","content":"There is a building with $n$ rooms, numbered $1$ to $n$.\nWe can move from any room to any other room in the building.\nLet us call the following event a **move**: a person in some room $i$ goes to another room $j~ (i \\neq j)$.\nInitially, there was one person in each room in the building.\nAfter that, we know that there were exactly $k$ moves happened up to now.\nWe are interested in the number of people in each of the $n$ rooms now. How many combinations of numbers of people in the $n$ rooms are possible?\nFind the count modulo $(10^9 + 7)$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $3 \\leq n \\leq 2 \\times 10^5$\n*   $2 \\leq k \\leq 10^9$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$n$ $k$"},{"iden":"sample input 1","content":"3 2"},{"iden":"sample output 1","content":"10\n\nLet $c_1$, $c_2$, and $c_3$ be the number of people in Room $1$, $2$, and $3$ now, respectively. There are $10$ possible combination of $(c_1, c_2, c_3)$:\n\n*   $(0, 0, 3)$\n*   $(0, 1, 2)$\n*   $(0, 2, 1)$\n*   $(0, 3, 0)$\n*   $(1, 0, 2)$\n*   $(1, 1, 1)$\n*   $(1, 2, 0)$\n*   $(2, 0, 1)$\n*   $(2, 1, 0)$\n*   $(3, 0, 0)$\n\nFor example, $(c_1, c_2, c_3)$ will be $(0, 1, 2)$ if the person in Room $1$ goes to Room $2$ and then one of the persons in Room $2$ goes to Room $3$."},{"iden":"sample input 2","content":"200000 1000000000"},{"iden":"sample output 2","content":"607923868\n\nPrint the count modulo $(10^9 + 7)$."},{"iden":"sample input 3","content":"15 6"},{"iden":"sample output 3","content":"22583772"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}