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 another room $j$ $(i\ne j)$. Initially, there was one person in each room in the building. After that, we know that there were exactly $k$ moves happened up to now. We 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? Find the count modulo $(10^9+7)$.

Input is given from Standard Input in the following format: > $n\quad k$ #### Constraints - All values in input are integers. - $3\le n\le 2\times 10^5$ - $2\le k\le 10^9$

Print the number of possible combinations of numbers of people in the $n$ rooms now, modulo $(10^9+7)$.

***For Sample #1:*** Let $c_1$, $c_2$, and $c_3$ be the number of people in Room $1$, $2$, and $3$ now, respectively. There are $10$ possible combination of $(c_1,c_2,c_3)$: - $(0,0,3)$ - $(0,1,2)$ - $(0,2,1)$ - $(0,3,0)$ - $(1,0,2)$ - $(1,1,1)$ - $(1,2,0)$ - $(2,0,1)$ - $(2,1,0)$ - $(3,0,0)$ For 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 $3$. ***For Sample #2:*** Print the count modulo $(10^9+7)$.

AtCoder [ABC156E]