import std.algorithm, std.container, std.conv, std.math, std.range, std.typecons, std.stdio, std.string; auto rdsp(){return readln.splitter;} void pick(R,T)(ref R r,ref T t){t=r.front.to!T;r.popFront;} void readV(T...)(ref T t){auto r=rdsp;foreach(ref v;t)pick(r,v);} const mod = 10^^9+7; alias mint = FactorRing!mod; alias Mat = Matrix!mint; void main() { long n; int m; readV(n, m); auto a = Mat([[1,1,0],[0,1,1],[0,1,0]]); auto b = Mat([[1,0,0],[0,1,1],[0,1,0]]); auto u = Mat.unit(3); writeln((a*b.repeatedSquare(m-1, u)).repeatedSquare(n, u)[0][1]); } pure T repeatedSquare(alias pred = "a * b", T, U)(T a, U n, T init) { import std.functional; alias predFun = binaryFun!pred; if (n == 0) return init; auto r = init; while (n > 0) { if (n&1) r = predFun(r, a); a = predFun(a, a); n >>= 1; } return r; } struct Matrix(T) { size_t r, c; T[][] a; alias a this; static ref auto unit(size_t n) { auto r = Matrix!T(n, n); foreach (i; 0..n) r[i][i] = 1; return r; } this(size_t r, size_t c) { this.r = r; this.c = c; a = new T[][](r, c); static if (T.init != 0) foreach (i; 0..r) a[i][] = 0; } this(U)(U[][] b) { r = b.length; c = b[0].length; a = new T[][](r, c); foreach (i; 0..r) foreach (j; 0..c) a[i][j] = b[i][j]; } ref auto dup() { auto x = Matrix!T(r, c); foreach (i; 0..r) x[i][] = a[i][]; return x; } ref auto opBinary(string op)(Matrix!T b) if (op == "+" || op == "-") in { assert(r == b.r && c == b.c); } body { auto x = Matrix!T(r, c); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = mixin("a[i][j]"~op~"b[i][j]"); return x; } ref auto opBinary(string op: "*")(Matrix!T b) in { assert(c == b.r); } body { auto x = Matrix!T(r, b.c); foreach (i; 0..r) foreach (j; 0..b.c) foreach (k; 0..c) x[i][j] += a[i][k]*b[k][j]; return x; } ref auto opBinary(string op: "*")(T[] b) in { assert(c == b.length); } body { auto x = new T[](r); static if (T.init != 0) x[] = 0; foreach (i; 0..r) foreach (j; 0..c) x[i] += a[i][j]*b[j]; return x; } } struct FactorRing(int m, bool pos = false) { version(BigEndian) union { long vl; struct { int vi2; int vi; } } else union { long vl; int vi; } alias FR = FactorRing!(m, pos); @property static init() { return FR(0); } @property int value() { return vi; } @property void value(int v) { vi = mod(v); } alias value this; this(int v) { vi = v; } this(int v, bool runMod) { vi = runMod ? mod(v) : v; } this(long v) { vi = mod(v); } ref auto opAssign(int v) { vi = v; return this; } pure auto mod(int v) const { static if (pos) return v%m; else return (v%m+m)%m; } pure auto mod(long v) const { static if (pos) return cast(int)(v%m); else return cast(int)((v%m+m)%m); } static if (!pos) pure ref auto opUnary(string op: "-")() { return FR(mod(-vi)); } static if (m < int.max / 2) { pure ref auto opBinary(string op)(int r) if (op == "+" || op == "-") { return FR(mod(mixin("vi"~op~"r"))); } ref auto opOpAssign(string op)(int r) if (op == "+" || op == "-") { vi = mod(mixin("vi"~op~"r")); return this; } } else { pure ref auto opBinary(string op)(int r) if (op == "+" || op == "-") { return FR(mod(mixin("vl"~op~"r"))); } ref auto opOpAssign(string op)(int r) if (op == "+" || op == "-") { vi = mod(mixin("vl"~op~"r")); return this; } } pure ref auto opBinary(string op: "*")(int r) { return FR(mod(vl*r)); } ref auto opOpAssign(string op: "*")(int r) { vi = mod(vl*r); return this; } pure ref auto opBinary(string op)(ref FR r) if (op == "+" || op == "-" || op == "*") { return opBinary!op(r.vi); } ref auto opOpAssign(string op)(ref FR r) if (op == "+" || op == "-" || op == "*") { return opOpAssign!op(r.vi); } }