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I HAVE A DOUBT REGARDING C PROBLEM. I WONDER HOW THIS SOLUTION WORKS??IT SHOULD FAIL BECAUSE- (first see the solution ,then read my doubt).

DOUBT- If we add some cards to the deck suppose "k".In this case the mx(highest frequency of card) may also increase??and we are checking for each possible size of deck (from 1 to n) that if the condition no.of decks>=mx holds.

(but mx can increase if we buy some card??then how this solution is working??)

// this is code

include <bits/stdc++.h>

using namespace std;

define ll long long

int main() { int t; cin >> t; while (t--) { ll n, k; cin >> n >> k; int chk=0; ll mx = -1,sum=0; vector a(n); for (ll i = 0; i < n; i++) { cin >> a[i]; sum+=a[i]; mx = max(mx, a[i]); }

ll ans=1;

    for (ll i = 1;i<=n; i++) {

        if (((sum+k)/i>=mx)&& (sum+k)/i * i >=sum) {
            //no. of deck>=mx & total cards>=sum

            ans=max(ans,i);
        }


    }
    cout << ans << endl;

}

}

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