I am facing Time Limit Exceeded in the problem Coin Combinations II of cses.

Code:

#include<bits/stdc++.h>
using namespace std;
#define ll long long 
#define nl '\n'
#define all(v) v.begin(), v.end()
#define IOS ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
const ll MOD = 1000000007;
int n, x, dp[1000001][101];
vector<int> c;
int rec(int x, int r){
	if(x == 0) return 1;
	if(x < 0 || r < 0) return 0;
	if(dp[x][r]!=-1) return dp[x][r];
	int ans = 0;
	ans += rec(x-c[r], r) + rec(x, r-1), ans%=MOD;
	return dp[x][r]=ans;
}
void solve(){
	cin >> n >> x; c.resize(n);
	for(int i=0; i<=x; ++i) for(int j=0; j<n; ++j) dp[i][j]=-1;
	for(int i=0; i<n; ++i) cin >> c[i];
	cout << rec(x, n-1);
}
signed main(){
	IOS
	solve();
}

My approach: We define rec(x, r) as the number of ordered ways to make a sum x by using up to rth coin (0-indexing). Now we are iterating from the last coin. We can either take rth coin and add up rec(x — c[r], r) to our answer or we can not take the rth coin and simply add up rec(x, r-1) (the answer by taking up to (r-1)th coin). So we have:

dp[i][j] = dp[i - c[j]][j] + dp[i][j - 1]

We also do dp[i][j] %= MOD to prevent overflow.

What could be the possible reason for Time Limit Exceeded? Thank you.

UPD: One person in the comments told that it is because constraints on CSES are tight and that's why recursion might give a TLE on CSES. I think that answers the question.

UPD: This is the exact reason for the TLE