Problem: Process the Q queries below.

* You are given two integers A_i and M_i. Determine whether there exists a positive integer K_i not exceeding 2 × 10^{18} such that A_i^{K_i} ≡ K_i (mod M_i), and find one if it exists.

Constraints

* 1 \leq Q \leq 100
* 0 \leq A_i \leq 10^9(1 \leq i \leq Q)
* 1 \leq M_i \leq 10^9(1 \leq i \leq Q)



Examples

Input

4
2 4
3 8
9 6
10 7


Output

4
11
9
2


Input

3
177 168
2028 88772
123456789 987654321


Output

7953
234831584
471523108231963269

Solution (in CPP):

Solution:
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 */
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
    
     
     
using namespace std;
template<typename T1, typename T2>inline void chkmin(T1 &x, T2 y) { if (x > y) x = y; }
template<typename T1, typename T2>inline void chkmax(T1 &x, T2 y) { if (x < y) x = y; }
/** Interface */
     
inline int readChar();
template <class T = int> inline T readInt(); 
template <class T> inline void writeInt( T x, char end = 0 );
inline void writeChar( int x ); 
inline void writeWord( const char *s );
     
/** Read */
     
static const int buf_size = 4096;
     
inline int getChar() {
    static char buf[buf_size];
    static int len = 0, pos = 0;
    if (pos == len) {
        pos = 0, len = fread(buf, 1, buf_size, stdin);
    }
    if (pos == len) {
        return -1;
    }
    return buf[pos++];
}
     
inline int readChar() {
    int c = getChar();
    while (c <= 32) {
        c = getChar();
    }
    return c;
}
     
template <class T>
inline T readInt() {
    int s = 1, c = readChar();
    T x = 0;
    if (c == '-')
        s = -1, c = getChar();
    while ('0' <= c && c <= '9')
        x = x * 10 + c - '0', c = getChar();
    return s == 1 ? x : -x;
}
     
/** Write */
     
static int write_pos = 0;
static char write_buf[buf_size];
     
inline void writeChar( int x ) {
    if (write_pos == buf_size)
        fwrite(write_buf, 1, buf_size, stdout), write_pos = 0;
    write_buf[write_pos++] = x;
}
     
template <class T> 
inline void writeInt( T x, char end ) {
    if (x < 0)
        writeChar('-'), x = -x;
     
    char s[24];
    int n = 0;
    while (x || !n)
        s[n++] = '0' + x % 10, x /= 10;
    while (n--)
        writeChar(s[n]);
    if (end)
        writeChar(end);
}
     
inline void writeWord( const char *s ) {     while (*s)
writeChar(*s++); }
     
struct Flusher {
    ~Flusher() {
        if (write_pos)
            fwrite(write_buf, 1, write_pos, stdout), write_pos = 0;
    }
} flusher;   
#define sz(c) (int)(c).size()
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define left left228
#define right right228
#define next next228
#define rank rank228
#define prev prev228
#define y1 y1228   


int Q;


long long Pow(long long a, long long b, long long Mod){
    long long r = 1;
    while(b) {
        if (b & 1) {
            r = r * a %Mod;
        }
        a = a * a % Mod;
        b >>= 1;
    }
    return r;
}


inline int Phi(int a) {
    int r = a;
    for (int i = 2; i * i <= a; i++) {
        if (a % i == 0){
            r = r / i * (i - 1);
            while (a % i == 0) {
                a /= i;
            }
        }
    }
    if (a != 1){
        r = r / a * (a - 1);
    }
    return r;
}


inline int gcd(int a, int b){
    return b ? gcd(b, a % b): a;
}


inline long long get(int a, int m){
    if (m <= 500) {
        int s = 1;
        for (int i = 1; ; i++) {
            s = 1LL * s * a % m;
            if (s == i % m) {
                return i;
            }
        }
        return -1;
    }
    int p = Phi(m);
    int g = gcd(m, p);
    long long r = get(a, g);
    if (r == -1) {
        return -1;
    }
    long long t = (Pow(a, r, m) + m - r) % m;
    int p2 = p / g, m2 = m / g;
    long long t2 = t / g;
    int pm = Phi(m2);
    long long ttt = 1LL * Pow(p2, pm - 1, m2) * t2 % m2;
    long long res = ttt * p + r;
    return res;
}


int main() {
    int q = readInt();
    while (q--) {
        int a = readInt(), m = readInt();
        printf("%lld\n", get(a, m));
    }
    return 0;
}