ntopia

dotorya, kesakiyo, and hongjun7 teach at an algorithm camp, and the three of them formed an idol group named ntopia.

The debut album of ntopia holds $S$ songs. Every song must be sung by at least one of the three. Two of them may sing a song together, and all three may sing one together.

Given the number of songs each of the three has to record, write a program that counts the ways to make the album.

Album $A$ and album $B$ are different albums if there is at least one song whose singers differ between them.

The first line contains the number of songs on the album, $S$, followed by the number of songs that dotorya, kesakiyo, and hongjun7 each have to sing, separated by spaces. ($1 \le S \le 10^6$, and each of the three song counts is between $1$ and $S$.)

Print on the first line the number of ways to make the album, modulo 1,000,000,007.