{"problem":{"name":"Roaming","description":{"content":"There is a building with $n$ rooms, numbered $1$ to $n$. We can move from any room to any other room in the building. Let us call the following event a **move**: a person in some room $i$ goes to anot","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc156_e"},"statements":[{"statement_type":"Markdown","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 $(10^9 + 7)$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $3 \\leq n \\leq 2 \\times 10^5$\n*   $2 \\leq k \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$n$ $k$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc156_e","tags":[],"sample_group":[["3 2","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 $3$."],["200000 1000000000","607923868\n\nPrint the count modulo $(10^9 + 7)$."],["15 6","22583772"]],"created_at":"2026-03-03 11:01:14"}}