using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Text; using System.Numerics; using System.Threading; using System.Runtime.CompilerServices; using System.Diagnostics; using static System.Math; using static System.Array; using static AtCoder.Cout; using static AtCoder.Tool; using static AtCoder.Graph; using static AtCoder.ModInt; namespace AtCoder { class AC { const int MOD = 1000000007; //const int MOD = 998244353; const int INF = int.MaxValue / 2; const long SINF = long.MaxValue / 3; static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 }; static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 }; static void Main(string[] args) { //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); /*var th = new Thread(Run, 1 << 26); th.Start(); th.Join();*/ Run(); Console.Out.Flush(); } static void Run() { int Testcase = 1; //Testcase = Cin.Int; for (var _ = 0; _ < Testcase; _++) Solve(); } static void Solve() { Cin.Scanf(out int N, out int K); var A = Cin.ReadSplitInt; for (var i = 0; i < N; i++) A[i] -= K; int s = 100 * N; var dp = new long[N + 1, 2 * s + 2]; dp[0, s] = 1; for(var i = 0; i < N; i++) { for(var j = 0; j <= 2 * s + 1; j++) { dp[i + 1, j] += dp[i, j]; dp[i + 1, j] %= MOD; if (0 <= j + A[i] && j + A[i] <= 2 * s + 1) { dp[i + 1, j + A[i]] += dp[i, j]; dp[i + 1, j + A[i]] %= MOD; } } } ModInt ans = 0; dp[N, s] = (dp[N, s] - 1 + MOD) % MOD; for (var i = s; i <= 2 * s + 1; i++) ans += dp[N, i]; OutL(ans); } } public struct Edge { public int from, to; public long w; public Edge(int to, long weight) { this.to = to; w = weight; from = -1; } public Edge(int from, int to, long weight) { this.from = from; this.to = to; w = weight; } } public class SCC { int n; struct Edge_S { public int from, to; public Edge_S(int f, int t) { from = f; to = t; } } List E; int[] id; public SCC(int size) { n = size; E = new List(); } public void Add_Edge(int from, int to) { E.Add(new Edge_S(from, to)); } public int[][] Scc_Result() { var start = new int[n + 1]; var nxt = new int[E.Count]; //var scc = new List>(); foreach (var ed in E) start[ed.from + 1]++; for (var i = 0; i < n; i++) start[i + 1] += start[i]; var itr = new int[n + 1]; for (var i = 0; i <= n; i++) itr[i] = start[i]; foreach (var ed in E) nxt[itr[ed.from]++] = ed.to; int now = 0; int[] ord = new int[n]; int[] low = new int[n]; id = new int[n]; var V = new Stack(); for (var i = 0; i < n; i++) ord[i] = -1; int nowid = 0; Action DFS = null; DFS = (v) => { low[v] = ord[v] = now++; V.Push(v); for (var i = start[v]; i < start[v + 1]; i++) { var nx = nxt[i]; if (ord[nx] == -1) { DFS(nx); low[v] = Min(low[v], low[nx]); } else { low[v] = Min(low[v], ord[nx]); } } if (low[v] == ord[v]) { while (true) { var u = V.Pop(); id[u] = nowid; ord[u] = n + 1; if (u == v) break; } nowid++; } }; for (var i = 0; i < n; i++) if (ord[i] == -1) DFS(i); for (var i = 0; i < n; i++) { id[i] = nowid - 1 - id[i]; itr[i] = 0; } var scc = new int[nowid][]; for (var i = 0; i < n; i++) itr[id[i]]++; for (var i = 0; i < nowid; i++) scc[i] = new int[itr[i]]; for (var i = 0; i < n; i++) scc[id[i]][--itr[id[i]]] = i; /* for (var i = 0; i < nowid; i++) scc.Add(new List()); for (var i = 0; i < n; i++) scc[id[i]].Add(i);*/ return scc; } public int v_id(int v) => id[v]; } public class LCA { List> G1; List> G2; int n; bool isweighted; int[] dist; long[] dist_w; int[,] par; public LCA(List> G) { G1 = G; G2 = null; n = G1.Count(); isweighted = false; dist = new int[n]; dist_w = null; par = new int[25, n]; } public LCA(List> G) { G1 = null; G2 = G; n = G2.Count(); isweighted = true; dist = new int[n]; dist_w = new long[n]; par = new int[25, n]; } public void Lca_Build(int root) { for (var i = 0; i < n; i++) { dist[i] = -1; if (isweighted) dist_w[i] = -1; } var dfs = new Stack(); dfs.Push(root); dist[root] = 0; if (isweighted) dist_w[root] = 0; par[0, root] = -1; while (dfs.Any()) { int v = dfs.Pop(); if (isweighted) { foreach (var ed in G2[v]) { if (dist[ed.to] != -1) continue; par[0, ed.to] = v; dist_w[ed.to] = dist[v] + ed.w; dist[ed.to] = dist[v] + 1; dfs.Push(ed.to); } } else { foreach (var nx in G1[v]) { if (dist[nx] != -1) continue; par[0, nx] = v; dist[nx] = dist[v] + 1; dfs.Push(nx); } } } for (var i = 1; i < 25; i++) { for (var j = 0; j < n; j++) { if (par[i - 1, j] == -1) par[i, j] = -1; else par[i, j] = par[i - 1, par[i - 1, j]]; } } } public int Lca(int u, int v) { if (dist[u] < dist[v]) { var kep = u; u = v; v = kep; } for (var i = 0; i < 30; i++) { if ((((dist[u] - dist[v]) >> i) & 1) != 0) { u = par[i, u]; } } if (u == v) return u; for (var i = 24; i >= 0; i--) { if (par[i, u] != par[i, v]) { u = par[i, u]; v = par[i, v]; } } return par[0, u]; } public int[] GetDist() => dist; public long[] GetWeightedDist() => dist_w; } struct ModInt { public long value; const int MOD = 1000000007; //const int MOD = 998244353; public ModInt(long value) { this.value = value; } public override string ToString() => value.ToString(); public static implicit operator ModInt(long a) { var ret = a % MOD; return new ModInt(ret < 0 ? (ret + MOD) : ret); } public static ModInt operator +(ModInt a, ModInt b) => (a.value + b.value); public static ModInt operator -(ModInt a, ModInt b) => (a.value - b.value); public static ModInt operator *(ModInt a, ModInt b) => (a.value * b.value); public static ModInt operator /(ModInt a, ModInt b) => a * Modpow(b, MOD - 2); public static ModInt operator <<(ModInt a, int n) => (a.value << n); public static ModInt operator >>(ModInt a, int n) => (a.value >> n); public static ModInt operator ++(ModInt a) => a.value + 1; public static ModInt operator --(ModInt a) => a.value - 1; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt Modpow(ModInt a, long n) { if (n == 0) return 1; if (n < 0) return Modpow(Modpow(a, -n), MOD - 2); var k = a; ModInt ret = 1; while (n > 0) { if ((n & 1) != 0) ret *= k; k *= k; n >>= 1; } return ret; } private static readonly List Factorials = new List() { 1 }; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt Fac(int n) { if (n < 0) return 0; for (var i = Factorials.Count(); i <= n; i++) { Factorials.Add((Factorials[i - 1] * i) % MOD); } return Factorials[n]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt nCr(int n, int r) { if (n < 0 || r < 0) return 0; return n < r ? 0 : Fac(n) / (Fac(r) * Fac(n - r)); } public static explicit operator int(ModInt a) => (int)a.value; } public static class Graph { const long inf = long.MaxValue / 3; public static List> Gen_Graph(int size) { var ret = new List>(); for (var i = 0; i < size; i++) ret.Add(new List()); return ret; } public static long[] Dijkstra(List> G, int st) { int N = G.Count(); long[] ret = new long[N]; var V = new Priority_Queue>((x, y) => Sig(x.Item1 - y.Item1)); for (var i = 0; i < N; i++) ret[i] = inf; ret[st] = 0; V.Enqueue(new Tuple(0, st)); while (V.Any()) { var cur = V.Dequeue(); int v = cur.Item2; long cd = cur.Item1; if (ret[v] < cd) continue; foreach (var ed in G[v]) { if (ret[ed.to] > cd + ed.w) { ret[ed.to] = cd + ed.w; V.Enqueue(new Tuple(ret[ed.to], ed.to)); } } } return ret; } public static long[] Bellman_Frod(List E, int st, int N, out bool neg_close) { var ret = new long[N]; for (var i = 0; i < N; i++) ret[i] = inf; ret[st] = 0; for (var i = 0; i < N; i++) { foreach (var ed in E) { if (ret[ed.from] != inf && ret[ed.to] > ret[ed.from] + ed.w) { if (i == N - 1) { neg_close = true; return ret; } ret[ed.to] = ret[ed.from] + ed.w; } } } neg_close = false; return ret; } } public class Priority_Queue { private List Q; private readonly Comparison Func_Compare; public Priority_Queue(Comparison comp) { Func_Compare = comp; Q = new List(); } private void PushHeap(T item) { int n = Q.Count(); Q.Add(item); while (n != 0) { int pIndex = (n - 1) / 2; if (Func_Compare(Q[n], Q[pIndex]) < 0) { Swap(n, pIndex); } else { break; } n = pIndex; } } private void PopHeap() { int n = Q.Count() - 1; Q[0] = Q[n]; Q.RemoveAt(n); int cur = 0; int comp; while (2 * cur + 1 <= n - 1) { int c1 = 2 * cur + 1; int c2 = 2 * (cur + 1); if (c1 == n - 1) { comp = c1; } else { comp = Func_Compare(Q[c1], Q[c2]) < 0 ? c1 : c2; } if (Func_Compare(Q[cur], Q[comp]) > 0) { Swap(cur, comp); } else { break; } cur = comp; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] private void Swap(int a, int b) { T keep = Q[a]; Q[a] = Q[b]; Q[b] = keep; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Enqueue(T value) => PushHeap(value); [MethodImpl(MethodImplOptions.AggressiveInlining)] public T Dequeue() { T ret = Q[0]; PopHeap(); return ret; } public T Peek() => Q[0]; public int Count() => Q.Count(); public bool Any() => Q.Any(); } public class SegmentTree { //1-indexed type int n; T[] Tree; Func f; T ex; int len; [MethodImpl(MethodImplOptions.AggressiveInlining)] public SegmentTree(int size, Func fun, T exvalue) { ex = exvalue; f = fun; len = size; n = 1; while (n < size) n <<= 1; Tree = new T[n << 1]; for (var i = 0; i < Tree.Length; i++) Tree[i] = ex; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Set_All() { for (var i = n - 1; i >= 1; i--) Tree[i] = f(Tree[i << 1], Tree[(i << 1) | 1]); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Assign(int idx, T nxt) => Tree[idx + n] = nxt; [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Update(int idx) { int now = idx + n; while (now > 1) { now >>= 1; Tree[now] = f(Tree[now << 1], Tree[now << 1 | 1]); } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Query_Update(int idx, T nxt) { Assign(idx, nxt); Update(idx); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Query_Update_func(int idx, T y) { Assign(idx, f(Peek(idx), y)); Update(idx); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public T Query_Fold(int l, int r) { int L = n + l; int R = n + r; T vL = ex, vR = ex; while (L < R) { if (L % 2 == 1) { vL = f(vL, Tree[L]); L++; } if (R % 2 == 1) { vR = f(Tree[R - 1], vR); R--; } L >>= 1; R >>= 1; } return f(vL, vR); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public T Peek(int idx) => Tree[idx + n]; [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Display(int len) { for (var i = 0; i < len; i++) Console.Write($"{Tree[i + n]} "); Console.WriteLine(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int MaxRight(int l, Func ok) { if (l == len) { return len; } l += n; var sum = ex; do { while (l % 2 == 0) l >>= 1; if (!ok(f(sum, Tree[l]))) { while (l < n) { l <<= 1; if (ok(f(sum, Tree[l]))) { sum = f(sum, Tree[l++]); } } return l - n; } sum = f(sum, Tree[l++]); } while ((l & (-l)) != l); return len; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int MinLeft(int r, Func ok) { if (r == 0) return 0; r += n; var sum = ex; do { r--; while (r > 1 && (r % 2) != 0) r >>= 1; if (!ok(f(Tree[r], sum))) { while (r < n) { r = (r << 1 | 1); if (ok(f(Tree[r], sum))) { sum = f(Tree[r--], sum); } } return r + 1 - n; } sum = f(Tree[r], sum); } while ((r & (-r)) != r); return 0; } } public class LazySegmentTree { int n, L; X[] Tree; A[] lazy; Func fxx; Func faa; Func fxa; X exx; A exa; public LazySegmentTree(int size, Func funcxx, Func funcaa, Func funcxa, X exval, A exlaz) { n = size; L = (n << 1) - 1; Tree = new X[n << 1]; lazy = new A[n << 1]; fxx = funcxx; faa = funcaa; fxa = funcxa; exx = exval; exa = exlaz; for (var i = 0; i <= L; i++) { Tree[i] = exx; lazy[i] = exa; } } public X eval(int id) => fxa(Tree[id], lazy[id]); [MethodImpl(MethodImplOptions.AggressiveInlining)] public void propagate(int id) { int h = 0; while ((1 << (h + 1)) <= id) h++; for (var n = h; n > 0; n--) { int i = id >> n; Tree[i] = eval(i); lazy[i << 1] = faa(lazy[i << 1], lazy[i]); lazy[i << 1 | 1] = faa(lazy[i << 1 | 1], lazy[i]); lazy[i] = exa; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void re_calc(int id) { while (id > 1) { id >>= 1; Tree[id] = fxx(eval(id << 1), eval(id << 1 | 1)); } } public void Range_Update(int l, int r, A op) { int L = n + l, R = n + r; int ll = L / (L & (-L)); int rr = R / (R & (-R)); propagate(ll); propagate(rr - 1); while (L < R) { if ((L & 1) == 1) { lazy[L] = faa(lazy[L], op); L++; } if ((R & 1) == 1) { R--; lazy[R] = faa(lazy[R], op); } L >>= 1; R >>= 1; } re_calc(ll); re_calc(rr - 1); } public X Range_Get(int l, int r) { int L = n + l, R = n + r; X vL = exx, vR = exx; propagate(L / (L & (-L))); propagate(R / (R & (-R)) - 1); while (L < R) { if ((L & 1) == 1) { vL = fxx(vL, eval(L)); L++; } if ((R & 1) == 1) { R--; vR = fxx(eval(R), vR); } L >>= 1; R >>= 1; } return fxx(vL, vR); } public void Point_Update(int idx, X nxt) { int id = idx + n; propagate(id); Tree[id] = nxt; re_calc(id); } /*======================*/ public void Assign(int idx, X nxt) => Tree[n + idx] = nxt; public void Set_All() { for (var i = n - 1; i >= 1; i--) { Tree[i] = fxx(Tree[i << 1], Tree[i << 1 | 1]); lazy[i] = faa(lazy[i << 1], lazy[i << 1 | 1]); } } public X Peek(int idx) => eval(idx); public void Display(int len) { for (var i = n; i < n + len; i++) Console.Write($"{eval(i)} "); Console.WriteLine(); } public void Displayall() { //木の形で表示、nが2冪でない時は注意 int e = 0; while ((1 << e) <= n) { for (var i = (1 << e); i < (1 << e) + (1 << e); i++) Console.Write($"{Tree[i]}/{lazy[i]} "); Console.WriteLine(); e++; } } } public class UnionFind { private int[] parent; private int[] rank; private int[] size; public UnionFind(int n) { parent = new int[n]; rank = new int[n]; size = new int[n]; for (var i = 0; i < n; i++) { parent[i] = i; rank[i] = 0; size[i] = 1; } } public int Root(int x) { return parent[x] == x ? x : parent[x] = Root(parent[x]); } public bool SameRoot(int x, int y) { return Root(x) == Root(y); } public void Unite(int x, int y) { x = Root(x); y = Root(y); if (x == y) { return; } if (rank[x] < rank[y]) { parent[x] = y; size[y] += size[x]; size[x] = 0; } else { parent[y] = x; if (rank[x] == rank[y]) { rank[x]++; } size[x] += size[y]; size[y] = 0; } } public int SizeOf(int x) { return size[Root(x)]; } } static class Cin { public static string[] ReadSplit => Console.ReadLine().Split(); public static int[] ReadSplitInt => ConvertAll(ReadSplit, int.Parse); public static long[] ReadSplitLong => ConvertAll(ReadSplit, long.Parse); public static double[] ReadSplit_Double => ConvertAll(ReadSplit, double.Parse); public static string Str => Console.ReadLine(); public static int Int => int.Parse(Console.ReadLine()); public static long Long => long.Parse(Console.ReadLine()); public static double Double => double.Parse(Console.ReadLine()); public static T Conv(string input) { if (typeof(T).Equals(typeof(ModInt))) { return (T)(dynamic)(long.Parse(input)); } return (T)Convert.ChangeType(input, typeof(T)); } public static void Scanf(out T a) => a = Conv(Console.ReadLine()); public static void Scanf(out T a, out U b) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); } public static void Scanf(out T a, out U b, out V c) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); } public static void Scanf(out T a, out U b, out V c, out W d) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); d = Conv(q[3]); } public static void Scanf(out T a, out U b, out V c, out W d, out X e) { var q = ReadSplit; a = Conv(q[0]); b = Conv(q[1]); c = Conv(q[2]); d = Conv(q[3]); e = Conv(q[4]); } } static class Cout { public static void OutL(object s) => Console.WriteLine(s); public static void Out_Sep(IEnumerable s) => Console.WriteLine(string.Join(" ", s)); public static void Out_Sep(IEnumerable s, string sep) => Console.WriteLine(string.Join($"{sep}", s)); public static void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s)); public static void Out_One(object s) => Console.Write($"{s} "); public static void Out_One(object s, string sep) => Console.Write($"{s}{sep}"); public static void Endl() => Console.WriteLine(); } public static class Tool { static public void Initialize(ref T[] array, T initialvalue) { array = ConvertAll(array, x => initialvalue); } static public void Swap(ref T a, ref T b) { T keep = a; a = b; b = keep; } static public void Display(T[,] array2d, int n, int m) { for (var i = 0; i < n; i++) { for (var j = 0; j < m; j++) { Console.Write($"{array2d[i, j]} "); } Console.WriteLine(); } } static public long Gcd(long a, long b) { if (a == 0 || b == 0) return Max(a, b); return a % b == 0 ? b : Gcd(b, a % b); } static public long LPow(int a, int b) => (long)Pow(a, b); static public bool Bit(long x, int dig) => ((1L << dig) & x) != 0; static public int Sig(long a) => a == 0 ? 0 : (int)(a / Abs(a)); } }