I have a lot of friends. Every friend is very small.
I often go out with my friends. Put some friends in your backpack and go out together.
Every morning I decide which friends to go out with that day. Put friends one by one in an empty backpack.
I'm not very strong. Therefore, there is a limit to the weight of friends that can be carried at the same time.
I keep friends so that I don't exceed the weight limit. The order in which you put them in depends on your mood.
I won't stop as long as I still have friends to put in. I will never stop.


…… By the way, how many patterns are there in total for the combination of friends in the backpack?



Input

N W
w1
w2
..
..
..
wn


On the first line of input, the integer N (1 ≤ N ≤ 200) and the integer W (1 ≤ W ≤ 10,000) are written in this order, separated by blanks. The integer N represents the number of friends, and the integer W represents the limit of the weight that can be carried at the same time. It cannot be carried if the total weight is greater than W.

The next N lines contain an integer that represents the weight of the friend. The integer wi (1 ≤ wi ≤ 10,000) represents the weight of the i-th friend.

Output

How many possible combinations of friends are finally in the backpack? Divide the total number by 1,000,000,007 and output the remainder. Note that 1,000,000,007 are prime numbers.

Note that "no one is in the backpack" is counted as one.

Examples

Input

4 8
1
2
7
9


Output

2


Input

4 25
20
15
20
15


Output

4


Input

6 37
5
9
13
18
26
33


Output

6
////////////////////
///   template   ///
////////////////////
#include <cassert>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <functional>
#include <vector>
#include <queue>
#include <string>
#include <complex>
#include <stack>
#include <set>
#include <map>
#include <list>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <regex>
using namespace std;

//// MACRO ////
#define countof(a) (sizeof(a)/sizeof(a[0]))

#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (s); i < (n); i++)
#define pos(c,i) c.being() + (i)
#define allof(c) c.begin(), c.end()
#define aallof(a) a, countof(a)
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)
#define apartof(a,i,n) a + (i), a + (i) + (n)
#define long long long

#define EPS 1e-10
#define INF 1000000000

#define PREDIACTE(t,a) [](const t & a) -> bool
#define COMPARISON_T(t) bool(*)(const t &, const t &)
#define COMPARISON(t,a,b) [](const t & a, const t & b) -> bool

//// algorithm ////

// compare
template <class InIt1, class InIt2>
int partial_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2)
{
	return lexicographical_compare(first1, last1, first2, last2) ? -1
		: lexicographical_compare(first2, last2, first1, last1) ? 1
		: 0;
}

// index_of
template <class InIt, class T>
inline int index_of(InIt first1, InIt last1, const T &val)
{
	InIt f = find(first1, last1, val);
	return f != last1 ? distance(f, first1) : -1;
}

// C# BinarySearch風のindex_of
template <class InIt, class T>
inline int bindex_of(InIt first1, InIt last1, const T &val)
{
	auto it = lower_bound(first1, last1, val);
	if (it == last1) { return ~distance(it, first1); }
	else if (*it == val) { return distance(it, first1); }
	else return ~distance(it, first1);
}

// vector iota iterator
vector<int> iotav(int begin, int end)
{
	vector<int> r(end - begin);
	iota(allof(r), begin);
	return r;
}

struct iotait
{
	int n;
	iotait(int n = 0) : n(n) { }
	iotait &operator ++() { ++n; return *this; }
	int operator *() { return n; }
};


// 最大公約数
long gcd(long a, long b) { return b ? gcd(b, a%b) : a; }

// 最小公倍数
long lcm(long a, long b) { return a / gcd(a, b) * b; }

// 拡張ユークリッド互除法
void exgcd(long a, long b, long& x, long& y) {
	if (b != 0) { exgcd(b, a%b, y, x); y -= a / b*x; }
	else { x = 1; y = 0; }
}

//// data structure ////

/// 2分セグメント木。RMQとかが解ける。
template<class T = int, class TParentFunc = const T& (*)(const T&, const T&)>
struct SegTree
{
	int count;
	vector<T> tree;
	TParentFunc parent;

	SegTree(int size, TParentFunc parentBuilder = std::min, T initialFill = INF)
		: count((size | size - 1) + 1)
		, tree(count * 2)
		, parent(parentBuilder)
	{
		fill(partof(tree, count, count), initialFill);
		rebuild();
	}

	// []を使うと更新されないのでrebuildすること。数が少なければupdateの方がよい。
	T& operator[](int i) { return tree[i + count]; }
	void rebuild() { RREP(i, count) { tree[i] = parent(tree[i * 2], tree[i * 2 + 1]); } }

	void update(int index, T value)
	{
		tree[index + count] = value;
		for (int i = (index + count) / 2; i > 0; i /= 2)
			tree[i] = parent(tree[i * 2], tree[i * 2 + 1]);
	}

	T query(int s, int e, int i, int l, int r, T value)
	{
		if (r <= s || e <= l) return value;
		if (s <= l && r <= e) return parent(value, tree[i]);
		value = query(s, e, i * 2, l, (l + r) / 2, value);
		value = query(s, e, i * 2 + 1, (l + r) / 2, r, value);
		return value;
	}

	T query(int start, int count, T initialValue)
	{
		return query(start, start + count, 1, 0, count, initialValue);
	}
};


//// prime ////
vector<unsigned char> isPrime;
vector<int> primes;
void initPrimes(int n)
{
	isPrime = vector<unsigned char>(n + 1, true);
	isPrime[0] = isPrime[1] = false;
	FOR(i, 2, n + 1)
	{
		if (!isPrime[i]) continue;
		primes.push_back(i);
		for (int j = i * 2; j <= n; j += i)
			isPrime[j] = false;
	}
}

//// Probability ////

// パスカルの三角形(二項定理) 2種類の並べ替えにつかう。
vector<vector<double>> makePascalTriangle(int n, bool probability = false)
{
	typedef vector<double> VD;
	vector<VD> t;
	if (!t.size()) { t.push_back(VD(1, 1)); }
	FOR(i, t.size(), n + 1)
	{
		t.push_back(VD(i + 1));
		REP(j, i)
		{
			double x = t[i - 1][j] * (probability ? 0.5 : 1);
			t[i][j] += x;
			t[i][j + 1] += x;
		}
	}
	return t;
}



//// geo ////

/// 3次元
struct P3
{
	double x, y, z;
	P3(double x = 0, double y = 0, double z = 0) : x(x), y(y), z(z) { }
	P3 operator +() const { return *this; }
	P3 operator +(const P3 &_) const { return P3(x + _.x, y + _.y, z + _.z); }
	P3 operator -() const { return P3(-x, -y, -z); }
	P3 operator -(const P3 &_) const { return *this + -_; }
	P3 operator *(double _) const { return P3(x*_, y*_, z*_); }
	P3 operator /(double _) const { return P3(x / _, y / _, z / _); }
	double dot(const P3 &_) const { return x*_.x + y*_.y + z*_.z; } // 内積
	P3 cross(const P3 &_) const { return P3(y*_.z - z*_.y, z*_.x - x*_.z, x*_.y - y*_.x); } // 外積
	double sqlength() const { return x*x + y*y + z*z; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P3 direction() const { return *this / length(); } // 方向ベクトル
};
inline istream & operator>>(istream & in, P3 & p) { in >> p.x >> p.y >> p.z; return in; }
inline double abs(P3 p) { return p.length(); }

struct Sphere
{
	P3 c;
	double r;
	Sphere(double x, double y, double z, double r) : c(x, y, z), r(r) { }
	Sphere(P3 c, double r) : c(c), r(r) { }
	bool IntersectWith(const Sphere &rhs) const { return abs(c - rhs.c) - (r + rhs.r) < EPS; } // 接してても真。
};
inline istream & operator>>(istream & in, Sphere & c) { in >> c.c >> c.r; return in; }

/// 2次元
struct P2
{
	double x, y;
	P2(double x = 0, double y = 0) : x(x), y(y) { }
	P2(complex<double> c) : x(c.real()), y(c.imag()) { }
	P2 operator +() const { return *this; }
	P2 operator +(const P2 &_) const { return P2(x + _.x, y + _.y); }
	P2 operator -() const { return P2(-x, -y); }
	P2 operator -(const P2 &_) const { return *this + -_; }
	P2 operator *(double _) const { return P2(x*_, y*_); }
	P2 operator /(double _) const { return P2(x / _, y / _); }
	double dot(const P2 &_) const { return x*_.x + y*_.y; } // 内積
	double cross(const P2 &_) const { return x*_.y - y*_.x; } // 外積
	double sqlength() const { return x*x + y*y; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P2 orthogonal() const { return P2(y, -x); }
	P2 direction() const { return *this / length(); } // 方向ベクトル
};
inline istream & operator>>(istream & in, P2 & p) { in >> p.x >> p.y; return in; }
inline double abs(P2 p2) { return p2.length(); }
inline P2 orthogonal(P2 p) { return p.orthogonal(); }
inline complex<double> orthogonal(complex<double> c) { return  c * complex<double>(0, 1); }

// a,b から ちょうど d だけ離れた点。aとbを円周に持つ円の半径。
inline pair<P2, P2> get_same_distance_points(P2 a, P2 b, double d)
{
	assert(abs(a - b) <= 2 * d + EPS);
	auto v = (a + b) / 2.0 - a; // a から aとbの中点
	auto vl = abs(v);
	auto wl = sqrt(d*d - vl*vl); // 直行Vの大きさ
	auto w = orthogonal(v) * (wl / vl); // 直行V
	return make_pair(a + v + w, a + v - w);
}

struct Circle
{
	P2 c;
	double r;
	Circle(double x, double y, double r) : c(x, y), r(r) { }
	Circle(P2 c, double r) : c(c), r(r) { }
	bool IntersectWith(const Circle &rhs) const { return abs(c - rhs.c) - (r + rhs.r) < EPS; } // 接してても真。
	bool Contains(const P2 &p) const { return abs(p - c) - r < EPS; } // 接してても真。
};
inline istream & operator>>(istream & in, Circle & c) { in >> c.c >> c.r; return in; }

//// bit ////
#ifdef _MSC_VER
#pragma push_macro("long")
#undef long
inline unsigned __builtin_ctz(unsigned x) { unsigned long r; _BitScanForward(&r, x); return r; }
#pragma pop_macro("long")
#endif

inline int next_bit_permutation(int x)
{
	int t = x | (x - 1);
	return (t + 1) | (unsigned)((~t & -~t) - 1) >> (__builtin_ctz(x) + 1);
}

// x の p1からlen bitと p2 から len bit を入れ替える
template<class T>
int bit_swap(T x, size_t p1, size_t p2, size_t len)
{
	T mask = (1ul << len) - 1;
	T ope = (x >> p1 ^ x >> p2) & mask; // 入れ替える場所のxorを求める
	return x ^ (ope << p1 | ope << p2); // 入れ替える場所をxor。
}

//// graph ////
struct Path
{
	int from;
	int to;
	double cost;
	double capacity;
	Path(int from = 0, int to = 0, double cost = 0, double capacity = -1)
		: from(from), to(to), cost(cost), capacity(capacity) { }
	bool operator < (const Path &rhs) const { return cost < rhs.cost; }
	bool operator >(const Path &rhs) const { return cost > rhs.cost; }
};

// prim //
pair<double, vector<int>> prim(const vector<vector<double>> &costTable)
{
	int N = costTable.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(0, 0, 0));

	vector<int> parent(N, -1);
	double totalCost = 0;
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (parent[i] != -1) continue;
		parent[i] = cur.from;
		totalCost += cur.cost;
		REP(j, N) if (parent[j] == -1) q.push(Path(i, j, costTable[i][j]));
	}
	return make_pair(totalCost, parent);
}

// dijkstra //
pair<vector<double>, vector<int>> dijkstra(const vector<vector<Path>> &routes, int start = 0, int goal = -1)
{
	int N = routes.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(start, start, 0));

	vector<int> prev(N, -1);
	vector<double> cost(N, INF);
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (prev[i] != -1) continue;
		prev[i] = cur.from;
		cost[i] = cur.cost;
		if (i == goal) { break; }
		REP(j, routes[i].size())
		{
			Path next = Path(i, routes[i][j].to, cur.cost + routes[i][j].cost);
			if (prev[next.to] == -1)
				q.push(next);
		}
	}
	return make_pair(cost, prev);
}

//// dice ////

// さいころ
template<class T>
struct Die
{
	/* v as 天一地六東五西二南三北四
	|3|
	|1|0|4|5|
	|2|
	*/
	T v[6];

	void rt(int x, int y, int z, int w) { swap(v[x], v[y]); swap(v[x], v[z]); swap(v[x], v[w]); }
	void rotateLeft() { rt(0, 4, 5, 1); }
	void rotateRight() { rt(1, 5, 4, 0); }
	void rotateDown() { rt(0, 3, 5, 2); }
	void rotateUp() { rt(2, 5, 3, 0); }
	void rotateCw() { rt(3, 1, 2, 4); }
	void rotateCcw() { rt(4, 2, 1, 3); }
	bool operator < (const Die &rhs) const { return lexicographical_compare(aallof(v), aallof(rhs.v)); }
	bool operator == (const Die &rhs) const { return equal(aallof(v), rhs.v); }
	bool operator != (const Die &rhs) const { return !equal(aallof(v), rhs.v); }
};

// 8面体
template<class T>
struct Octahedra
{
	/* v as
	/0\/1\/2\/3\
	\4/\5/\6/\7/
	*/
	T v[8];

	void rt(int x, int y, int z, int w) { swap(v[x], v[y]); swap(v[x], v[z]); swap(v[x], v[w]); }
	void rotateLeft() { rt(0, 1, 2, 3); rt(4, 5, 6, 7); }
	void rotateRight() { rt(3, 2, 1, 0); rt(7, 6, 5, 4); }
	void rotateDown() { rt(0, 4, 7, 3); rt(1, 5, 6, 2); }
	void rotateUp() { rt(3, 7, 4, 0); rt(2, 6, 5, 2); }
	void rotateCw() { rt(0, 1, 5, 4); rt(3, 2, 6, 7); }
	void rotateCcw() { rt(4, 5, 1, 0); rt(7, 6, 1, 3); }
	bool operator < (const Octahedra &rhs) const { return lexicographical_compare(aallof(v), aallof(rhs.v)); }
	bool operator == (const Octahedra &rhs) const { return equal(aallof(v), rhs.v); }
	bool operator != (const Octahedra &rhs) const { return !equal(aallof(v), rhs.v); }
};



//// i/o ////
template <class T>
class vevector : public vector<vector<T>>
{
public:
	vevector(int n = 0, int m = 0) : vector<vector<T>>(n, vector<T>(m)) { };
	vevector(int n, int m, const T &initial) : vector<vector<T>>(n, vector<T>(m, initial)) { };
};

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(read<T>(read<int>())); return v; }
struct _Reader { template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
#define READ(t,...) t __VA_ARGS__; _Reader(), __VA_ARGS__

template <class T> void write(const T &t) { cout << t << endl; }
template <class T, class T2> void write(const T &t, const T2 &t2) { cout << t << ' ' << t2 << endl; }
template <class T> void write(const vector<T> &v)
{
	ostringstream ss;
	for (auto x : v) ss << x << ' ';
	auto s = ss.str();
	cout << s.substr(0, s.length() - 1) << endl;
}


//// start up ////
void solve();
int main()
{
	// freopen("A.in", "r", stdin);
	solve();
	return 0;
}

////////////////////
/// template end ///
////////////////////

#define MOD 1000000007

int dfs(const vector <int> &we, const vector<int> &wsum, vector<vevector<int>> &memo, int cur, int weight, int weLastSkiped, vector<int> &dbg)
{
	if (cur == -1)
	{
		if (weight >= we[weLastSkiped]) { return 0; } // とらなくてはいけないアイテムをとってない。
		//write(dbg);
		return 1;
	}

	if (memo[cur][weight][weLastSkiped] != -1) { return memo[cur][weight][weLastSkiped]; }

	// のこりのアイテムをすべてとっても、かばんに余裕ができてしまう。
	if (we[weLastSkiped] + wsum[cur] <= weight)
	{
		memo[cur][weight][weLastSkiped] = 0;
		return 0;
	}

	int pat = 0;
	// かばんにはいる
	if (weight >= we[cur])
	{
		dbg.push_back(we[cur]);
		pat += dfs(we, wsum, memo, cur - 1, weight - we[cur], weLastSkiped, dbg);
		dbg.pop_back();
	}

	// かばんにいれない
	{
		pat += dfs(we, wsum, memo, cur - 1, weight, cur, dbg);
	}

	return memo[cur][weight][weLastSkiped] = pat % MOD;
}

void solve()
{
	auto testcases = INF; // read<int>();
	REP(testcase, testcases)
	{
		READ(int, n, w);
		auto we = read<int>(n);
		we.push_back(INF); n++;
		sort(allof(we));

		auto wesum = vector<int>();
		partial_sum(allof(we), back_inserter(wesum));
		
		vector<vevector<int>> memo(n + 1, vevector<int>(w + 1, n + 1, -1));

		int ret = dfs(we, wesum, memo, n - 2, w, n - 1, vector<int>());
		write(ret);

		break;
	}
}