#include<iostream>
#include<cstring>
#include<vector>
#include<numeric>
#include<map>
#include<algorithm>
using namespace std;
using LL = long long;
map<pair<int, int>, LL> dp[13][1 << 13];

int f[1 << 13][500];

int main(){

#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif

    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);

    int n, m;
    cin >> n >> m;
    vector<int> a(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
    }
    pair<int, int> mx{0, 0};
    for(int i = 0; i < n; i++){
        mx = max(mx, make_pair(a[i], -i));
    }
    for(int i = 0; i < n; i++){
        int need = mx.first - a[i];
        if (make_pair(a[i] + need, -i) < mx){
            need += 1;
        }
        if (need * n <= m) dp[i][1 << i][{need, need}] = 1;
    }

    auto get = [&](int state, int last){
        
        vector<int> v;
        for(int i = 0; i < n; i++){
            if (!(state >> i & 1)){
                v.push_back(i);
            }
        }

        int l = 0, r = 0;    
        for(auto x : v){
            l += a[last] - a[x];
        }
        sort(v.begin(), v.end(), [&](int x, int y){
            return a[x] < a[y];
        });
        {
            vector<int> nv;
            for(int i = 0, j = n - 1; i <= j; i++, j--){
                nv.push_back(i);
                if (i != j) nv.push_back(j);
            }
            v.swap(nv);
        }
        int lastval = a[last];
        int val = -1e9;
        for(auto x : v){
            int need = max(lastval + 1 - a[x], val + 1);
            r += need;
            val = need;
            lastval = a[x] + need;
        }
        return make_pair(l, r);
    };

    LL fact[14];
    fact[0] = 1;
    for(int i = 1; i <= 13; i++) fact[i] = fact[i - 1] * i;
    LL ans = 0;

    for(int i = 1; i + 1 < 1 << n; i++){
        int c = __builtin_popcount(i);
        for(int j = 0; j < n; j++){

            auto [l, r] = get(i, j);

            for(auto &[par, cnt] : dp[j][i]){
                auto [last, sum] = par;
                if (sum + l + last * (n - c) > m){
                    continue;
                }
                if (sum + r + last * (n - c) <= m){
                    ans += fact[n - c] * cnt;
                    continue;
                }
                pair<int, int> mx = {a[j] + last, -j};
                for(int k = 0; k < n; k++){
                    if (i >> k & 1) continue;
                    int need = max(last, a[j] + last - a[k]);
                    if (pair(a[k] + need, -k) < mx){
                        need += 1;
                    }
                    if ((n - c) * need + sum <= m){
                        dp[k][i | (1 << k)][{need, need + sum}] += cnt;
                    }
                }
            }
        }
    }
    for(int i = 0; i < n; i++){
        for(auto &[par, cnt] : dp[i][(1 << n) - 1]){
            ans += cnt;
        }
    }
    cout << ans << '\n';

}