Problem:
Score : 600 points

Problem Statement

AtCoDeer the deer has N cards with positive integers written on them. The number on the i-th card (1≤i≤N) is a_i.
Because he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.

Then, for each card i, he judges whether it is unnecessary or not, as follows:

If, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.

Otherwise, card i is NOT unnecessary.

Find the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary.

Constraints

All input values are integers.

1≤N≤5000

1≤K≤5000

1≤a_i≤10^9 (1≤i≤N)

Partial Score

300 points will be awarded for passing the test set satisfying N,K≤400.

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the number of the unnecessary cards.

Sample Input 1

3 6
1 4 3

Sample Output 1

1

There are two good sets: {2,3} and {1,2,3}.

Card 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.

For card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.

Neither is card 3 for a similar reason, hence the answer is 1.

Sample Input 2

5 400
3 1 4 1 5

Sample Output 2

5

In this case, there is no good set. Therefore, all the cards are unnecessary.

Sample Input 3

6 20
10 4 3 10 25 2

Sample Output 3

3

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static

#define rep(i,n) for(ll i=0LL;i<n;++i)
#define srep(i,s,n) for(ll i=s;i<n;++i)
#define rrep(i,n) for(ll i=n-1LL;i>=0LL;--i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
    assert(!cin.eof()); \
    cin >> x; \
    assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T>>;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

struct UnionFind
{
    ull *parent, *count, *rank;

    UnionFind(ull n) {
        parent = new ull[n+1];
        count = new ull[n+1];
        rank = new ull[n+1];
        for (ull i = 0ULL; i < n+1; ++i) {
            parent[i] = i;
            count[i] = 1;
            rank[i] = 0;
        }
    }

    ~UnionFind() {
        delete rank;
        delete count;
        delete parent;
    }

    ull root(ull i) {
        if (parent[i] == i) return i;
        parent[i] = root(parent[i]);
        return parent[i];
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (rank[rootj] < rank[rooti]) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] += count[rootj];
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] += count[rooti];
            if (rank[rootj] == rank[rooti]) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct UnionFindM
{
    M<ull, ull> parent, count, rank;

    ull root(ull i) {
        ull parent_i = get_m(parent, i, i);
        if (parent_i == i) return i;
        return parent[i] = root(parent_i);
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (get_m(rank, rootj, 0ULL) < get_m(rank, rooti, 0ULL)) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] = get_m(count, rooti, 1ULL) + get_m(count, rootj, 1ULL);
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] = get_m(count, rootj, 1ULL) + get_m(count, rooti, 1ULL);
            if (get_m(rank, rootj, 0ULL) == get_m(rank, rooti, 0ULL)) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct BIT
{
    ll *tree;
    ll size;

    BIT(ll n, ll init) {
        tree = new ll[n+1];
        size = n;
        this->init(init);
    }

    void init(ll init) {
        memset(tree, 0, sizeof(ll) * (size+1));
        rep (i0, size) {
            ll idx = i0 + 1LL;
            while (idx <= size) {
                tree[idx] += init;
                idx += (idx & (-idx));
            }
        }
    }

    // idx is 1 origin
    void add(ll idx, ll x) {
        assert(idx > 0LL);
        while (idx <= size) {
            tree[idx] += x;
            idx += (idx & (-idx));
        }
    }

    // idx is 1 origin
    ll sum(ll idx) {
        assert(idx > 0LL);
        ll ret = 0LL;
        while (idx > 0LL) {
            ret += tree[idx];
            idx -= (idx & (-idx));
        }
        return ret;
    }
};

struct MaxFlow {
    V<ll> links[1005];
    ll capacities[1005][1005];
    ll nodes;

    MaxFlow(ll nodes) {
        // i == 0       --> S
        // i == nodes+1 --> T
        rep (i, nodes+2LL) links[i].clear();
        memset(capacities, 0, sizeof(capacities));
        this->nodes = nodes;
    }

    void add_path(ll a, ll b, ll capacity) {
        links[a].pb(b);
        links[b].pb(a);
        capacities[a][b] = capacity;
        capacities[b][a] = 0LL;
    }

    ll solve(void) {
        deque<V<ll>> q;
        ll ret = 0LL;

        for ( ; ; q.clear()) {

            V<ll> start;
            start.pb(0);
            q.push_front(start);

            bool checked[nodes+2];
            memset(checked, 0, sizeof(checked));

            V<ll> found;

            for ( ; !(q.empty()); ) {
                V<ll> path = q.front(); q.pop_front();
                ll last = path[path.size()-1];

                if (checked[last]) continue;
                if (last == nodes+1) {
                    found = path;
                    break;
                }

                checked[last] = true;
                for (auto next : (links[last])) {
                    if (capacities[last][next] == 0) continue;
                    V<ll> newpath(path);
                    newpath.pb(next);
                    q.push_front(newpath);
                }
            }

            if (found.size() == 0) {
                break;
            }
            else {
                ll flowcount = capacities[found[0]][found[1]];
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    flowcount = min(flowcount, capacities[src][dst]);
                }
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    capacities[src][dst] -= flowcount;
                    capacities[dst][src] += flowcount;
                }
                ret += flowcount;
            }
        }

        return ret;
    }
};

template <typename T>
struct SegmentTree {
    T *nodes;
    t2 *ranges;  // [start, end)
    ll nodecount;
    ll itemcount;
    T unit;
    T (*op)(T, T);

    SegmentTree(ll itemcount, T unit, T op(T, T)) {
        ll orig_itemcount = itemcount;
        this->itemcount = 1LL;
        while (this->itemcount < orig_itemcount) this->itemcount *= 2LL;
        nodecount = this->itemcount * 2 - 1;
        nodes = new T[nodecount];
        ranges = new t2[nodecount];
        this->unit = unit;
        this->op = op;

        ll start = 0LL;
        ll end = this->itemcount;
        ll len = this->itemcount;

        rep (i, nodecount) {
            nodes[i] = unit;
            ranges[i] = t2(start, end);
            if (end >= this->itemcount) {
                len /= 2LL;
                start = 0LL;
                end = len;
            }
            else {
                start = end;
                end = start + len;
            }
        }
    }

    void update(ll k, T v) {
        ll idx = k + itemcount - 1LL;
        nodes[idx] = v;
        idx = (idx - 1LL) / 2LL;

        for ( ; idx >= 0; idx = (idx - 1LL) / 2LL) {
            nodes[idx] = op(nodes[idx * 2LL + 1LL],
                            nodes[idx * 2LL + 2LL]);
            if (!idx) break;
        }
    }

    // query to [start, end)
    T query(ll start, ll end) const {
        return _query(start, end, 0LL);
    }

    T _query(ll start, ll end, ll idx) const {
        ll rstart = get<0>(ranges[idx]);
        ll rend = get<1>(ranges[idx]);

        if (start <= rstart && rend <= end) {
            return nodes[idx];
        }
        if (rend <= start || end <= rstart) {
            return unit;
        }
        T left = _query(start, end, idx * 2LL + 1LL);
        T right = _query(start, end, idx * 2LL + 2LL);
        return op(left, right);
    }

};

void llin(ll &a)
{
    CIN(a);
}

void llinl1(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(auto &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
T min(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = min(ret, i);
    return ret;
}

template <typename T>
T max(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = max(ret, i);
    return ret;
}

ll absll(ll x)
{
    if (x < 0) return -x;
    return x;
}

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ll gcm(ll x, ll y)
{
    while (y != 0) {
        ll z = x % y;
        x = y;
        y = z;
    }
    return x;
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

void get_divisors(V<ll> &retlist, ll x)
{
    for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
        if (x % i == 0LL) {
            retlist.push_back(i);
            retlist.push_back(x / i);
        }
    }
}

// returns factors and 1
void get_factors(V<ll> &retlist, ll x)
{
    retlist.pb(1LL);
    for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
        while (x % i == 0LL) {
            retlist.pb(i);
            x /= i;
        }
    }
    retlist.pb(x);
}

bool is_prime(ll x)
{
    V<ll> factors, factors2;

    get_factors(factors, x);

    for (auto factor : factors) {
        if (factor > 1) factors2.pb(factor);
    }

    return factors2.size() == 1 && x == factors2[0];
}

template <typename T>
void intersection(const set<T> &a, const set<T> &b,
                  set<T> &result)
{
    set_intersection(ALL(a), ALL(b), inserter(result, result.end()));
}

ull combination(ll x, ll y)
{
    if (y > x / 2LL) y = x - y;

    ull ret = 1LL;
    for (ll i = 0LL; i < y; ++i) {
        ret *= x--;
        ret /= (i + 1LL);
    }

    return ret;
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
   }

    rep (i, size) {
        perm_invs[i] = mod_inv(perms[i], mod);
    }
}

void make_linklist(const V<t2> &srclist, V<ll> dstlist[])
{
    for (auto src : srclist) {
        ll a = get<0>(src);
        ll b = get<1>(src);
        dstlist[a].pb(b);
        dstlist[b].pb(a);
    }
}

void make_parental_relation(const V<ll> linklist[], ll root, ll n,
                            ll parent[], V<ll> children[], ll level[])
{
    queue<ll> q;
    bool checked[n+1];

    memset(checked, 0, sizeof(checked));

    q.push(root);
    checked[root] = true;
    parent[root] = root;
    level[root] = 0LL;

    for ( ; !(q.empty()); ) {
        ll now = q.front(); q.pop();
        for (auto next : linklist[now]) {
            if (checked[next]) continue;
            q.push(next);
            checked[next] = true;
            parent[next] = now;
            children[now].pb(next);
            level[next] = level[now] + 1LL;
        }
    }
}

void make_subtree_sizes(const ll child_count[], const ll parents[],
                        ll subtree_sizes[], ll n)
{
    ll remain_count[n+1LL];
    memcpy(remain_count, child_count, sizeof(remain_count));

    queue<ll> q;
    srep (node, 1LL, n+1LL) {
        subtree_sizes[node] = 1LL;
        if (remain_count[node] > 0) continue;
        q.push(node);
    }

    while (!q.empty()) {
        ll node = q.front(); q.pop();
        ll parent = parents[node];
        if (node == parent) continue;
        remain_count[parent]--;
        subtree_sizes[parent] += subtree_sizes[node];
        if (remain_count[parent] == 0LL) q.push(parent);
    }
}

void get_centroids(const V<ll> children[], const ll subtree_sizes[],
                   ll root, ll n, V<ll> &centroids)
{
    queue<ll> q;
    q.push(root);

    while (!q.empty()) {
        ll now = q.front(); q.pop();
        bool is_centroid = true;
        for (auto child : children[now]) {
            q.push(child);
            if (subtree_sizes[child] > n / 2LL) is_centroid = false;
        }
        if (n - subtree_sizes[now] > n / 2LL) is_centroid = false;
        if (is_centroid) centroids.pb(now);
    }

    assert(centroids.size() == 1LL || centroids.size() == 2LL);
}

#define POW_ANCESTOR_MAXSIZE   20

// preprocess for get_common_ancestor()
void make_pow_ancestor(const ll parent[], ll n,
                       ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE])
{
    rep (i, n) pow_ancestor[i+1][0] = parent[i+1];

    for (int pow2 = 1; pow(2, pow2) <= n; ++pow2) {
        rep (i0, n) {
            int i = i0+1;
            ll prev = pow_ancestor[i][pow2-1];
            pow_ancestor[i][pow2] = pow_ancestor[prev][pow2-1];
        }
    }
}

ll get_common_ancestor(ll n, ll x, ll y,
                       const ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE],
                       const ll level[])
{
    if (level[x] < level[y]) {
        ll diff = level[y] - level[x];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            y = pow_ancestor[y][(int)log2(bit)];
            diff -= bit;
        }
    }
    else {
        ll diff = level[x] - level[y];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            x = pow_ancestor[x][(int)log2(bit)];
            diff -= bit;
        }
    }

    if (x == y) return x;

    rrep (i, (int)log2(n)+1) {
        if (pow_ancestor[x][i] != pow_ancestor[y][i]) {
            x = pow_ancestor[x][i];
            y = pow_ancestor[y][i];
        }
    }

    return pow_ancestor[x][0];
}

void kmp_init(const string &pattern, ll kmp_next[])
{
    kmp_next[0] = -1LL;

    ll plen = pattern.size();
    ll prefix_end = -1;

    rep (suffix_end, pattern.size()) {
        while (prefix_end >= 0 && pattern[suffix_end] != pattern[prefix_end]) {
            prefix_end = kmp_next[prefix_end];
        }
        kmp_next[suffix_end+1] = ++prefix_end;
    }

    kmp_next[0] = 0LL;
}

// founds ... list of text's idx of match position. start position idx.
void kmp_search(const string &text, const string &pattern, const ll kmp_next[],
                V<ll> &founds)
{
    ll text_size = text.size();
    ll pattern_size = pattern.size();
    ll text_start = 0LL;
    ll pattern_idx = 0LL;

    assert(pattern_size <= text_size);

    for ( ; ; ) {
        if (text_start + pattern_idx >= text_size) break;
        if (pattern_idx >= pattern_size) break;

        if (text[text_start+pattern_idx] == pattern[pattern_idx]) {
            pattern_idx++;
            if (pattern_idx == pattern_size) {
                founds.pb(text_start);
                pattern_idx = kmp_next[pattern_idx];
                text_start += (pattern_size - pattern_idx);
            }
        }

        else {
            text_start += (pattern_idx - kmp_next[pattern_idx]);
            pattern_idx = kmp_next[pattern_idx];
            if (pattern_idx == 0LL && text[text_start] != pattern[0]) {
                text_start++;
            }
        }
    }
}

void z_algorithm(ll matchcounts[], const string &str)
{
    ll n = str.size();
    ll base_idx = 0LL;
    memset(matchcounts, 0, sizeof(ll) * n);

    srep (idx, 1LL, n) {

        ll checked_len = base_idx + matchcounts[base_idx];

        if (idx + matchcounts[idx-base_idx] < checked_len) {
            matchcounts[idx] = matchcounts[idx-base_idx];
            continue;
        }

        ll start = max(0LL, base_idx + matchcounts[base_idx] - idx);
        matchcounts[idx] = start;
        srep (cmp, start, n-idx) {
            if (str[cmp] == str[idx+cmp]) matchcounts[idx]++;
            else break;
        }
        base_idx = idx;

    }

    matchcounts[0] = n;
}

void _debug_print(auto x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
        << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    struct tm *tm = localtime(&tv.tv_sec);
    printf("-- %s %02d:%02d:%02d.%06ld\n",
           prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}

///////////////////////////////////////////////////////////////////////////////

bool judge(const V<ll> &alist, ll n, ll k, ll idx)
{
    bitset<5005> bs;
    bs.set(0);

    rep (i, n) {
        if (i == idx) continue;
        ll a = alist[i];
        bitset<5005> bs_orig = bs;
        bs <<= a;
        bs |= bs_orig;
    }

    srep (i, k-alist[idx], k) {
        if (bs.test(i)) return false;
    }

    return true;
}

void _main();
int main()
{
    cout << setprecision(12);
    _main();
    return 0;
}

void _main()
{
    ll n; llin(n);
    ll k; llin(k);
    S V<ll> alist; llina(alist, n);

    alist.pb(0LL);
    n++;
    sort(alist);

    ll left = 0LL;
    ll right = n-1LL;
    ll now = (left + right) / 2LL;
    ll ans = 0LL;

    for ( ; left <= right; now = (left + right) / 2LL) {
        if (judge(alist, n, k, now)) {
            ans = max(ans, now);
            left = now + 1LL;
        }
        else {
            right = now - 1LL;
        }
    }

    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////