import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = x_ % M; } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 10^^9 + 7; alias Mint = ModInt!MO; // square matrices Mint[][] mul(Mint[][] a, Mint[][] b) { const size = cast(int)(a.length); auto c = new Mint[][](size, size); foreach (i; 0 .. size) foreach (k; 0 .. size) foreach (j; 0 .. size) { c[i][j] += a[i][k] * b[k][j]; } return c; } Mint[] mul(Mint[][] a, Mint[] x) { const size = cast(int)(a.length); auto y = new Mint[size]; foreach (i; 0 .. size) foreach (j; 0 .. size) { y[i] += a[i][j] * x[j]; } return y; } Mint[][] power(Mint[][] a, long e) { const size = cast(int)(a.length); auto b = new Mint[][](size, size), c = new Mint[][](size, size); foreach (i; 0 .. size) foreach (j; 0 .. size) b[i][j] = a[i][j]; foreach (i; 0 .. size) foreach (j; 0 .. size) c[i][j] = (i == j) ? 1 : 0; for (; e; e >>= 1) { if (e & 1) c = mul(c, b); b = mul(b, b); } return c; } void main() { try { for (; ; ) { const L = readLong; const N = readInt; const M = readInt; auto K = new int[M]; foreach (m; 0 .. M) { K[m] = readInt; } int V; auto ids = new int[][](N + 1, N + 2); foreach (x; 0 .. N + 1) { ids[x][] = -1; } int[] xs, ys; foreach (x; 1 .. N + 1) { foreach (y; 1 .. (x + 1) + 1) { ids[x][y] = V++; xs ~= x; ys ~= y; } } debug { writeln("ids = ", ids); writeln("xs = ", xs); writeln("ys = ", ys); } auto good = new bool[V]; foreach (k; K) { good[ids[k][k]] = true; } auto a = new Mint[][](V + 1, V + 1); foreach (u; 0 .. V) { foreach (xx; 1 .. N + 1) { const yy = (xs[u] == xx) ? min(ys[u] + 1, xx + 1) : 1; const v = (good[u] && xs[u] != xx) ? V : ids[xx][yy]; debug { if (N <= 3) { writeln(u, " ", xx, ": ", v); } } a[u][v] += 1; } } a[V][V] += N; debug { if (N <= 3) { writeln("a = ", a); } } const aa = a.power(L - 1); Mint ans; foreach (x; 1 .. N + 1) { const u = ids[x][1]; foreach (v; 0 .. V + 1) { if (v == V || good[v]) { ans += aa[u][v]; } } } writeln(ans); } } catch (EOFException e) { } }