Shared code

//! We can go up or down, either ways I am prepared

//! Hello there! Subhadeep this side.

#include<bits/stdc++.h>
using namespace std;

#define fastio() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define MOD 1000000007
#define MOD1 998244353
#define INF 1e18
#define nline "\n"
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define ff first
#define ss second
#define PI 3.141592653589793238462
#define set_bits __builtin_popcountll
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define mid(low, high) (low + ((high - low) >> 1))

typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
// typedef tree<pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update > pbds; // find_by_order, order_of_key

#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif

void _print(ll t) {cerr << t;}
void _print(int t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(lld t) {cerr << t;}
void _print(double t) {cerr << t;}
void _print(ull t) {cerr << t;}

template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.ff); cerr << ","; _print(p.ss); cerr << "}";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {_print(i); cerr << " ";} cerr << "]";}


template<class T> inline  T nxt(T) {
    T x;
    cin >> x;
    return x;
}

ll n, target;
ll coins[105];
ll dp[105][1000100];

int answer(int level, int goal) {
    // pruning
    
    // base case
    if(goal == target) return 1; 
    if(level >= n) return 0;
    
    // cache check
    if(dp[level][goal] != -1) return dp[level][goal];
    
    // transition / compute
    int take = 0, nottake = 0;
    
    if(goal + coins[level] <= target)
        take += answer(level, goal + coins[level]);
    nottake += answer(level+1, goal);
    
    // save and return
    dp[level][goal] = take + nottake;
    
    return dp[level][goal];
}

void solve() {
    cin >> n >> target;
    for (int i = 0; i < n; i++) cin >> coins[i];
    
    memset(dp, -1, sizeof(dp));
    cout << answer(0,0) << nline;    
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("Error.txt", "w", stderr);
#endif

fastio();
    int t=1;
    // cin>>t;
    while(t--) {
        solve();
    }
    
    return 0;
}