package main import ( "bufio" "fmt" "os" "strconv" ) func getScanner(fp *os.File) *bufio.Scanner { scanner := bufio.NewScanner(fp) scanner.Split(bufio.ScanWords) scanner.Buffer(make([]byte, 1000005), 1000005) return scanner } func getNextString(scanner *bufio.Scanner) string { scanner.Scan() return scanner.Text() } func getNextInt(scanner *bufio.Scanner) int { i, _ := strconv.Atoi(getNextString(scanner)) return i } func getNextInt64(scanner *bufio.Scanner) int64 { i, _ := strconv.ParseInt(getNextString(scanner), 10, 64) return i } func getNextUint64(scanner *bufio.Scanner) uint64 { i, _ := strconv.ParseUint(getNextString(scanner), 10, 64) return i } func getNextFloat64(scanner *bufio.Scanner) float64 { i, _ := strconv.ParseFloat(getNextString(scanner), 64) return i } func main() { fp := os.Stdin wfp := os.Stdout cnt := 0 if os.Getenv("MASPY") == "ますピ" { fp, _ = os.Open(os.Getenv("BEET_THE_HARMONY_OF_PERFECT")) cnt = 2 } if os.Getenv("MASPYPY") == "ますピッピ" { wfp, _ = os.Create(os.Getenv("NGTKANA_IS_GENIUS10")) } scanner := getScanner(fp) writer := bufio.NewWriter(wfp) solve(scanner, writer) for i := 0; i < cnt; i++ { fmt.Fprintln(writer, "-----------------------------------") solve(scanner, writer) } writer.Flush() } func solve(scanner *bufio.Scanner, writer *bufio.Writer) { n := getNextInt(scanner) w := getNextInt(scanner) k := getNextInt64(scanner) aa := make([]int, n) for i := 0; i < n; i++ { aa[i] = getNextInt(scanner) } dp1 := make([]mint, w+1) dp1[0] = 1 for i := 0; i < w; i++ { for j := 0; j < n && i+aa[j] < w+1; j++ { dp1[i+aa[j]].addAs(dp1[i]) } } dp2 := make([]mint, w<<1+1) dp2[0] = 1 for i := 0; i < w<<1; i++ { for j := 0; j < n && i+aa[j] < w<<1+1; j++ { if i+aa[j] == w { continue } dp2[i+aa[j]].addAs(dp2[i]) } } ini := make([]mint, 2) ini[0] = dp1[w] ini[1] = 1 mat := makeGrid(2, 2) mat[0][0] = dp1[w] mat[0][1] = 1 mat[1][0] = dp2[w<<1] for i := 0; i < 60; i++ { if (k-1)>>uint(i)%2 == 1 { ini0 := ini[0].mul(mat[0][0]).add(ini[1].mul(mat[1][0])) ini1 := ini[0].mul(mat[0][1]).add(ini[1].mul(mat[1][1])) ini[0] = ini0 ini[1] = ini1 } mat00 := mat[0][0].mul(mat[0][0]).add(mat[0][1].mul(mat[1][0])) mat01 := mat[0][0].mul(mat[0][1]).add(mat[0][1].mul(mat[1][1])) mat10 := mat[1][0].mul(mat[0][0]).add(mat[1][1].mul(mat[1][0])) mat11 := mat[1][0].mul(mat[0][1]).add(mat[1][1].mul(mat[1][1])) mat[0][0] = mat00 mat[0][1] = mat01 mat[1][0] = mat10 mat[1][1] = mat11 } fmt.Fprintln(writer, ini[0]) } func makeGrid(h, w int) [][]mint { index := make([][]mint, h, h) data := make([]mint, h*w, h*w) for i := 0; i < h; i++ { index[i] = data[i*w : (i+1)*w] } return index } type mint int64 func (mt mint) mod() mint { m := mint(1e9 + 7) mt %= m if mt < 0 { return mt + m } return mt } func (mt mint) inv() mint { var m, y mint m.subAs(2) dbl := mt y = 1 for i := 0; i < 31; i++ { if m%2 == 1 { y.mulAs(dbl) } m >>= 1 dbl.mulAs(dbl) } return y } func (mt mint) add(x mint) mint { return (mt + x).mod() } func (mt mint) sub(x mint) mint { return (mt - x).mod() } func (mt mint) mul(x mint) mint { return (mt * x).mod() } func (mt mint) div(x mint) mint { return mt.mul(x.inv()) } func (mt *mint) addAs(x mint) *mint { *mt = mt.add(x) return mt } func (mt *mint) subAs(x mint) *mint { *mt = mt.sub(x) return mt } func (mt *mint) mulAs(x mint) *mint { *mt = mt.mul(x) return mt } func (mt *mint) divAs(x mint) *mint { *mt = mt.div(x) return mt }