coin_combinations_2.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 = 1 * 1000000 + 10; // 1e6


int ddp(int n,vector<int>&coins,vector<ll>&dp) {
    dp[0] = 1;

    for (int j = 0; j < sz(coins); ++j) {
        for (int i = 0; i <= n; ++i) {
            if(i-coins[j] >= 0)
            dp[i] = ((dp[i-coins[j]]%mod) + (dp[i]%mod))%mod;
        }
    }

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

    for (int j = 0; j < n; ++j) {
        cin >> coins[j];
    }
    vector<ll>dp(x+1,0);
    ddp(x,coins,dp);
    cout << dp[x] << endl;
    return 0;

}