jerry99的序列 --binary search, math

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
const int N = 1e5 + 10;
const int M = N - 10;
int tot, vis[N], prime[N];
//#define LOCAL

void sieve () {
    for (int i = 2; i <= M; ++i) {
        if (!vis[i])
            prime[tot++] = i;
        for (int j = 0; j < tot; ++j) {
            if (1LL * prime[j] * i > M)
                break;
            vis[i * prime[j]] = 1;
            if (i % prime[j] == 0)
                break;
        }
    }
}

bool check(int mid, vector<pair<int, int>> &factor) {
    for (auto it : factor) {
        int prime = it.first;
        int cnt = it.second;
        i64 tmp = 1, res = 0;
        while (tmp <= mid) {
            tmp *= prime;
            res += mid / tmp;
        }
#ifdef LOCAL
        cout << "res: " << res << "\n";
#endif
        if (res < cnt)
            return true;
    }
    return false;
}
int n, m;

void solve() {

    if (n == 1) {
        cout << m << "\n";
        return ;
    }
    int l = 1, r = m + 1;
    vector<pair<int, int>> factor;
    int tmp = n;
    for (int i = 0; i < tot && prime[i] * prime[i] <= tmp; ++i) {
        if (tmp % prime[i] == 0) {
            int cnt = 0;
            while (tmp % prime[i] == 0) {
                cnt++;
                tmp /= prime[i];
            }
            factor.emplace_back(prime[i], cnt);
        }
    }
    if (tmp > 1) {
        factor.emplace_back(tmp, 1);
    }
#ifdef LOCAL
    for (auto [x, y] : factor) {
        cout << x << ' ' << y << "\n";
    }
#endif
    while (l < r) {
        int mid = l + r >> 1;
        if (check(mid, factor)) {
            l = mid + 1;
        } else {
            r = mid;
        }
    }
#ifdef LOCAL
    cout << "l: " << l << "\n";
#endif
    cout << m - l + 1 << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t;
    cin >> t;
    sieve();
    for (; t--;) {
        cin >> n >> m;
        solve();
    }

    return 0;
}