// URL: https://yukicoder.me/problems/no/194 import std.algorithm, std.array, std.bitmanip, std.container, std.conv, std.format, std.functional, std.math, std.range, std.traits, std.typecons, std.stdio, std.string; version(unittest) {} else void main() { int N; long K; io.getV(N, K); int[] A; io.getA(N, A); if (K <= 10^^6) { auto f = new mint[](K); foreach (i, Ai; A) f[i] = Ai; f[N] = f[0..N].sum; foreach (i; N+1..K) f[i] = f[i-1]*2-f[i-N-1]; io.put(f[$-1], f.sum); } else { auto m = Matrix!mint(N+1, N+1); foreach (i; 1..N) m[i-1][i] = 1; foreach (i; 0..N) { m[N-1][i] = 1; m[N][i] = 1; } m[N][N] = 1; auto v = Vector!mint(N+1); foreach (i, Ai; A) v[i] = Ai; v[N] = v[0..N].sum; auto r = m^^(K-N)*v; io.put(r[N-1], r[N]); } } pure nothrow @safe { T powr(alias pred = "a*b", T, U)(const T a, U n, T one) if (isIntegral!U) { auto b = T(a); alias predFun = binaryFun!pred; if (n == 0) return one; auto r = one; for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, b); b = predFun(b, b); } return r; } T powr(alias pred = "a*b", T, U)(const T a, U n) if (isIntegral!U) { return powr!(pred, T, U)(a, n, T(1)); } } struct Vector(T) { size_t n; @property T[] array() { return a; } alias array this; pure nothrow @safe { this(size_t n, T zero = T(0)) in { assert(n > 0); } do { this.n = n; this.zero = zero; a = new T[](n); if (T.init != zero) foreach (i; 0..n) a[i] = zero; } this(U)(U[] b, T zero = T(0)) in { assert(b.length > 0); } do { n = b.length; this.zero = zero; static if (is(T == U)) { a = b; } else { a = new T[](n); foreach (i; 0..n) a[i] = b[i]; } } this(ref return scope const Vector!T v) { n = v.n; zero = v.zero; a = new T[](n); foreach (i; 0..n) a[i] = v.a[i]; } Vector!T dup() const { return Vector!T(this); } Vector!T opBinary(string op)(const Vector!T b) const if (op == "+" || op == "-") in { assert(n == b.n); } do { auto x = Vector!T(n, zero); foreach (i; 0..n) x[i] = mixin("a[i]"~op~"b.a[i]"); return x; } ref Vector!T opOpAssign(string op)(const Vector!T b) if (op == "+" || op == "-") in { assert(n == b.n); } do { foreach (i; 0..n) mixin("a[i]"~op~"=b.a[i];"); return this; } Vector!T opBinary(string op: "*", U)(U b) const if (isNumeric!T) { auto x = Vector!T(n, zero); foreach (i; 0..n) x[i] = a[i]*b; return x; } ref Vector!T opOpAssign(string op: "*", U)(U b) if (isNumeric!T) { foreach (i; 0..n) a[i] *= b; return this; } T opBinary(string op: "*")(const Vector!T b) const in { assert(n == b.n); } do { auto x = T(zero); foreach (i; 0..n) x += a[i]*b.a[i]; return x; } } private { T[] a; T zero; } } pure nothrow @safe { auto vector(T)(T[] a, T zero = T(0)) { return Vector!T(a, zero); } T hypot2(T)(const Vector!T a) { return a*a; } pure Vector!T cross(T)(Vector!T a, Vector!T b) in { assert(a.n == 3 && b.n == 3); } do { return Vector!T([a[1]*b[2]-a[2]*b[1], a[2]*b[0]-a[0]*b[2], a[0]*b[1]-a[1]*b[0]], a.zero); } } struct Matrix(T) { size_t r, c; @property T[][] array() { return a; } alias array this; pure nothrow @safe { static Matrix!T unit(size_t n, T zero = T(0), T one = T(1)) in { assert(n > 0); } do { auto r = Matrix!T(n, n, zero, one); foreach (i; 0..n) r[i][i] = one; return r; } this(size_t r, size_t c, T zero = T(0), T one = T(1)) in { assert(r > 0 && c > 0); } do { this.r = r; this.c = c; this.zero = zero; this.one = one; a = new T[][](r, c); if (T.init != zero) foreach (i; 0..r) foreach (j; 0..c) a[i][j] = zero; } this(U)(U[][] b, T zero = T(0), T one = T(1)) in { assert(b.length > 0 && b[0].length > 0 && b.all!(l => l.length == b[0].length)); } do { r = b.length; c = b[0].length; this.zero = zero; this.one = one; static if (is(T == U)) { a = b; } else { a = new T[][](r, c); foreach (i; 0..r) foreach (j; 0..c) a[i][j] = b[i][j]; } } this(ref return scope const Matrix!T v) { r = v.r; c = v.c; zero = v.zero; one = v.one; a = new T[][](r, c); foreach (i; 0..r) foreach (j; 0..c) a[i][j] = v.a[i][j]; } Matrix!T dup() const { return Matrix!T(this); } bool opEquals(Matrix!T b) const { return r == b.r && c == b.c && zip(a, b.a).all!"a[0]==a[1]"; } Matrix!T opBinary(string op)(const Matrix!T b) const if (op == "+" || op == "-") in { assert(r == b.r && c == b.c); } do { auto x = Matrix!T(r, c, zero, one); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = mixin("a[i][j]"~op~"b.a[i][j]"); return x; } ref Matrix!T opOpAssign(string op)(const Matrix!T b) if (op == "+" || op == "-") in { assert(r == b.r && c == b.c); } do { foreach (i; 0..r) foreach (j; 0..c) mixin("a[i][j]"~op~"=b.a[i][j];"); return this; } Matrix!T opBinary(string op: "*", U)(U b) const if (isNumeric!U) { auto x = Matrix!T(r, c, zero, one); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = a[i][j]*b; return x; } ref Matrix!T opOpAssign(string op: "*", U)(U b) if (isNumeric!U) { foreach (i; 0..r) foreach (j; 0..c) a[i][j] *= b; return this; } Matrix!T opBinary(string op: "*")(const Matrix!T b) const in { assert(c == b.r); } do { auto x = Matrix!T(r, b.c, zero, one); foreach (i; 0..r) foreach (j; 0..b.c) foreach (k; 0..c) x[i][j] += a[i][k]*b.a[k][j]; return x; } ref Matrix!T opOpAssign(string op: "*")(const Matrix!T b) in { assert(c == b.r); } do { auto x = this*b; r = x.r; c = x.c; a = x.a; return this; } Vector!T opBinary(string op: "*")(const Vector!T b) const in { assert(c == b.n); } do { auto x = Vector!T(r, zero); foreach (i; 0..r) foreach (j; 0..c) x[i] += a[i][j]*b.a[j]; return x; } Matrix!T opBinary(string op: "^^", U)(U n) const if (isIntegral!U) in { assert(r == c); } do { return powr(this, n, Matrix!T.unit(r, zero, one)); } } private { T[][] a; T zero, one; } } pure nothrow @safe { auto matrix(T)(T[][] a, T zero = T(0), T one = T(1)) { return Matrix!T(a, zero, one); } T det(T)(Matrix!T a) in { assert(a.r == a.c); } do { auto n = a.r, b = a.dup, d = a.one; foreach (i; 0..n) { auto p = i; foreach (j; i+1..n) if (b[p][i].abs < b[j][i].abs) p = j; swap(b[p], b[i]); foreach (j; i+1..n) foreach (k; i+1..n) b[j][k] -= b[i][k]*b[j][i]/b[i][i]; d *= b[i][i]; if (p != i) d = -d; } return d; } } const mod = 10^^9+7; alias mint = ModInt!mod; pure nothrow @nogc @safe { auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } } pure nothrow @nogc @safe { T cdiv(T)(const T a, const T b) { return (a+b-1)/b; } T pmod(T)(const T a, const T b) { return a >= 0 ? a%b : a%b+b; } ExtGcdResult!T extGcd(T)(const T a, const T b) { if (a == 0) { return ExtGcdResult!T(T(b), T(0), T(1)); } else { auto r = extGcd(b%a, a); return ExtGcdResult!T(r.gcd, r.y-(b/a)*r.x, r.x); } } private struct ExtGcdResult(T) { T gcd, x, y; } } struct ModInt(int m, bool pos = false) { pure nothrow @nogc @safe { @property int value() { return i; } @property void value(int v) { i = nm(v); } alias value this; this(T)(T v) if (isIntegral!T) { i = nm(v); } this(ref return scope const Mint v) { i = v.i; } ref Mint opAssign(T)(T v) if (isIntegral!T) { i = nm(v); return this; } ref Mint opAssign(const Mint v) { i = v.i; return this; } static if (!pos) { Mint opUnary(string op: "-")() const { return Mint(-i); } } static if (m < int.max / 2) { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("i"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("i"~op~"r")); return this; } } else { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("l"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("l"~op~"r")); return this; } } Mint opBinary(string op: "*", T)(T r) const if (isIntegral!T) { return Mint(l*r); } ref Mint opOpAssign(string op: "*", T)(T r) if (isIntegral!T) { i = nm(l*r); return this; } Mint opBinary(string op)(const Mint r) const if (op == "+" || !pos && op == "-" || op == "*") { return opBinary!op(r.i); } ref Mint opOpAssign(string op)(const Mint r) if (op == "+"|| !pos && op == "-" || op == "*") { return opOpAssign!op(r.i); } Mint opBinary(string op: "^^", T)(T n) if (isIntegral!T) { return powr(this, n, Mint(1)); } static if (!pos) { Mint opBinary(string op: "/")(const Mint r) const { return Mint(l*r.inv.i); } ref Mint opOpAssign(string op: "/")(const Mint r) { i = nm(l*r.inv.i); return this; } Mint opBinary(string op: "/", T)(T r) const if (isIntegral!T) { return opBinary!op(Mint(r)); } Mint opOpAssign(string op: "/", T)(T r) if (isIntegral!T) { return opOpAssign!op(Mint(r)); } Mint inv() const { return Mint(extGcd(i, m).x); } } } private { alias Mint = ModInt!(m, pos); version(BigEndian) union { long l; struct { int i2; int i; } } else union { long l; int i; } pure nothrow @nogc @safe { int nm(T)(T v) const if (isIntegral!T) { static if (pos) return cast(int)(v%m); else return cast(int)pmod(v, m); } } } } auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.meta : allSatisfy; import core.stdc.stdlib : exit; void getV(T...)(ref T v) { foreach (ref w; v) get(w); } void getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } void getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } void getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { void getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } const struct PutConf { bool newline = true, flush, exit; string floatFormat = "%.10f", delimiter = " "; } void put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } void putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } void putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } void get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } void putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i+1 < v.length) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } void putOne(PutConf c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putRange!c(v); else static if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else static if (hasMember!(T, "fprint")) v.fprint(OUT); else OUT.write(v); } void putRange(PutConf c, T)(T v) { auto w = v; while (!w.empty) { putOne!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } } }