A_Add_and_Divide.cpp

#include <bits/stdc++.h>
#include <algorithm>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
// Add the necessary include paths to the compiler flags
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")

#define nl '\n'
#define sp ' '
#define pi 2 * acos(0.0)

// Control Flow
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i, a, b) for (int i = (b) - 1; i >= a; i--)
#define F0Rd(i, a) for (int i = (a) - 1; i >= 0; i--)
#define trav(a, x) for (auto &a : x)

// Types of declarations
#define ui unsigned int
#define us unsigned short
#define ull unsigned long long
#define ll long long
#define ld long double
#define vstr vector<string>
#define vll vector<ll>
#define vi vector<int>
#define vvi vector<vector<int>>
#define vii vector<pair<int, int>>
#define pii pair<int, int>

// Utils
#define len(x) int((x).size())
#define pb push_back
#define all(n) n.begin(), n.end()
#define rall(n) n.rbegin(), n.rend()

// Constants
const ll MOD = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

// Odd Even
bool odd(ll num) { return ((num & 1) == 1); }
bool even(ll num) { return ((num & 1) == 0); }

// Prime check
bool isPrime(int n)
{
    for (int i = 2; i * i <= n; i++)
    {
        if (n % i == 0)
            return false;
    }
    return true;
}

// GCD & LCM
long long gcd(long long a, long long b)
{
    while (b != 0)
    {
        long long temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}
long long lcm(long long a, long long b)
{
    return (a / gcd(a, b)) * b;
}

// Square Root
long long sqrt(long long x)
{
    long long s = 0, e = 2e9, res = s;
    while (s <= e)
    {
        long long m = (s + e) / 2;
        if (m * m <= x)
            res = m, s = m + 1;
        else
            e = m - 1;
    }
    return res;
}

void solve()
{

    ll a, b;
    cin >> a >> b;

    // Performing increments first is always a better idea;
    // You will be able to destroy 'a' quickly!

    // worst case: a=1e9, b=1 -> b=2, a=1e9 (1ops) -> log(1e9) ~ 30
    // Using calculus, b <= 6
    ll ans = 1e9;
    for (int i = 0; i <= 10; i++)
    {
        ll x = a;
        if (b + i >= 2)
        {
            ll turns = i;
            while (x > 0)
            {
                x = x / (b + i);
                turns++;
            }
            ans = min(turns, ans);
        }
    }
    cout << ans << nl;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);

    int t = 1;
    cin >> t;
    while (t--)
        solve();

    return 0;
}