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 solve1(N, K int, a []int) { K = min(1000000, K) sum := 0 for i := 0; i < N; i++ { sum += a[i] } f := sum s := sum for i := N; i < K; i++ { f = sum s += sum s %= mod // out(f, s) x := a[i%N] a[i%N] = sum sum += sum - x sum %= mod if sum < 0 { sum += mod } } out(f, s) } func mulMod(A, B [][]int) [][]int { H := len(A) W := len(B[0]) K := len(A[0]) C := make([][]int, W) for i := 0; i < W; i++ { C[i] = make([]int, W) } for i := 0; i < H; i++ { for j := 0; j < W; j++ { for k := 0; k < K; k++ { C[i][j] += A[i][k] * B[k][j] C[i][j] %= mod } } } return C } func powModMatrix(A [][]int, p int) [][]int { N := len(A) ret := make([][]int, N) for i := 0; i < N; i++ { ret[i] = make([]int, N) ret[i][i] = 1 } for p > 0 { if p&1 == 1 { ret = mulMod(ret, A) } A = mulMod(A, A) p >>= 1 } return ret } func solve2(N, K int, x []int) { a := make([][]int, N) for i := 0; i < N; i++ { a[i] = make([]int, N) } for i := 0; i < N; i++ { a[0][i] = 1 } for i := 1; i < N; i++ { a[i][i-1] = 1 } a = powModMatrix(a, K-N) f := 0 for i := 0; i < N; i++ { f += x[N-1-i] * a[0][i] f %= mod } a = make([][]int, N+1) for i := 0; i < N+1; i++ { a[i] = make([]int, N+1) } a[0][0] = 2 a[0][N] = -1 for i := 1; i < N+1; i++ { a[i][i-1] = 1 } // for i := 0; i < N+1; i++ { // out(a[i]) // } a = powModMatrix(a, K-N) y := make([]int, N+1) y[0] = 0 for i := 1; i < N+1; i++ { y[i] = y[i-1] + x[i-1] } // out(y) s := 0 for i := 0; i < N+1; i++ { s += y[N-i] * a[0][i] s %= mod } out(f, s) } func main() { sc.Split(bufio.ScanWords) N, K := getInt(), getInt() a := getInts(N) if K > 100000 { solve2(N, K, a) } else { solve1(N, K, a) } }