package main import ( "bufio" "fmt" "os" "sort" "strconv" ) func out(x ...interface{}) { fmt.Println(x...) } var sc = bufio.NewScanner(os.Stdin) func getInt() int { sc.Scan() i, e := strconv.Atoi(sc.Text()) if e != nil { panic(e) } return i } func getInts(N int) []int { ret := make([]int, N) for i := 0; i < N; i++ { ret[i] = getInt() } return ret } func getString() string { sc.Scan() return sc.Text() } // min, max, asub, absなど基本関数 func max(a, b int) int { if a > b { return a } return b } func min(a, b int) int { if a < b { return a } return b } func asub(a, b int) int { if a > b { return a - b } return b - a } func abs(a int) int { if a >= 0 { return a } return -a } func lowerBound(a []int, x int) int { idx := sort.Search(len(a), func(i int) bool { return a[i] >= x }) return idx } func upperBound(a []int, x int) int { idx := sort.Search(len(a), func(i int) bool { return a[i] > x }) return idx } const mod = int(1e9 + 7) func gcd(a, b int) int { if b == 0 { return a } return gcd(b, a%b) } func powmod(a, p int) int { if p == 0 { return 1 } if p%2 == 1 { return powmod(a, p-1) * a % mod } mid := powmod(a, p/2) return mid * mid % mod } func rev(a int) int { return powmod(a, mod-2) } func main() { sc.Split(bufio.ScanWords) K := getInt() C := make([]int, K) sum := 0 for i := 0; i < K; i++ { C[i] = getInt() sum += C[i] } g := C[0] for i := 0; i < K; i++ { g = gcd(g, C[i]) } ans := 0 factor := make([]int, 0) num := make([]int, 0) for i := g; i >= 1; i-- { if g%i != 0 { continue } remain := sum/i - 1 mul := 1 div := 1 for j := 0; j < K; j++ { end := 0 if j == 0 { end = 1 } for l := 0; l < C[j]/i-end; l++ { mul *= remain remain-- mul %= mod div *= l + 1 div %= mod } } mul *= rev(div) for j := 0; j < len(factor); j++ { if factor[j]%i != 0 { continue } mul -= num[j] } mul %= mod mul += mod mul %= mod num = append(num, mul) mul *= rev(C[0] / i) mul %= mod factor = append(factor, i) ans += mul ans %= mod } out(ans) }