coin_combinations_1.cpp

//Author: kaiyu
#include <iostream>
#include <algorithm>
#include <cmath>
#include <map>
#include <vector>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cstring>
#include <string>
#include <queue>
#include <stack>
#include <numeric>
#include <iomanip>
#include <climits>
using namespace std;
typedef long long ll;
#define sz(x) ((long long)(x).size())
#define all(x)  x.begin(),x.end()
#define endl "\n"
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define mod             1000000007 //1e9+7
#define vi vector<ll>
#define vvi vector<vector<ll>>
#define pii pair<int,int>
#define tt ll t;cin >> t;while(t--)
#define int3(x,y,z) ll x,y,z;cin >> x >> y >> z;
#define int2(x,y) ll x,y;cin >> x >>y;
#define int1(x) ll x;cin>>x;
#define  fio ios::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL);
ll power(ll a,ll b,ll m=mod){ ll ans=1; a=a%m;  while(b>0) {  if(b&1)  ans=(1ll*a*ans)%m; b>>=1;a=(1ll*a*a)%m;}return ans;}

ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}


bool cmp(pair<string,int>p1,pair<string,int>p2) {
    return p1.ss > p2.ss;
}

const int MAXN = 5 * 1000000 + 10; // 1e6
ll dp[MAXN];
int ddp(int n,vector<int>&coins) {

    if(n==0) {
        return dp[n]=1;
    }
    if(n<0) {
        return 0;
    }
    if(dp[n] != -1) {
        return dp[n];
    }
    ll ways = 0;
    for (auto i : coins) {
        ways = ((ways%mod)+(ddp(n - i,coins)%mod))%mod;
    }
    return dp[n]=ways;
}

int32_t main() {
    fio
    int x,n;
    cin >> x >> n;
    vector<int>coins(x);

    for (int j = 0; j < x; ++j) {
        cin >> coins[j];
    }

    for (long long & i : dp) {
        i = -1;
    }

    ddp(n,coins);
    cout << dp[n] << endl;
}