using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Trace; using SB = System.Text.StringBuilder; using static System.Math; using static Program.IO.Scanner; using Number = System.Int64; using System.Numerics; #region IO namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { } } static public class Scanner { public static StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); public static int ri => sc.Integer(); public static long rl => sc.Long(); public static string rs => sc.Scan(); public static double rd => sc.Double(); } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); } public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); } public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); } } } #endregion #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(ie.ToArray()); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false }); var solver = new Program.Solver(); var t = new System.Threading.Thread(solver.Solve, 50000000); t.Start(); t.Join(); //*/ //solver.Solve(); Console.Out.Flush(); } } #endregion namespace Program { public class Solver { Random rnd = new Random(0); public void Solve() { var q = ri; for (int i = 0; i < q; i++) { var p = rl; var v = p - 1; v *= v; ModInt.Mod = p; var res = ModInt.Pow(2, v) - v; if (res.num != 0) throw new Exception(); if (p == 2) Console.WriteLine(2); else Console.WriteLine(v); } } const long INF = 1L << 60; static int[] dx = { -1, 0, 1, 0 }; static int[] dy = { 0, 1, 0, -1 }; static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < a.Length; ++i) a[i] = f(i); return a; } static T[][] Enumerate(int n, int m, Func f) { return Enumerate(n, x => Enumerate(m, y => f(x, y))); } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region ModInt /// /// [0,) までの値を取るような数 /// public struct ModInt { /// /// 剰余を取る値. /// public static long Mod = (int)1e9 + 7; /// /// 実際の数値. /// public long num; /// /// 値が であるようなインスタンスを構築します. /// /// インスタンスが持つ値 /// パフォーマンスの問題上,コンストラクタ内では剰余を取りません.そのため, ∈ [0,) を満たすような を渡してください.このコンストラクタは O(1) で実行されます. public ModInt(long n) { num = n; } /// /// このインスタンスの数値を文字列に変換します. /// /// [0,) の範囲内の整数を 10 進表記したもの. public override string ToString() { return num.ToString(); } public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; } public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; } public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); } public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); } /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); } /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(long v, long k) { long ret = 1; for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod) if ((k & 1) == 1) ret = ret * v % Mod; return new ModInt(ret); } /// /// 与えられた数の逆元を計算します. /// /// 逆元を取る対象となる数 /// 逆元となるような値 /// 法が素数であることを仮定して,フェルマーの小定理に従って逆元を O(log N) で計算します. public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); } } #endregion #region PrimeSieve public static partial class MathEx { /// /// Finding all the prime numbers in [1,n]. Time complexity: O(N loglog N) /// public static bool[] Sieve(int N) { var ret = new bool[N + 1]; for (int i = 2; i < ret.Length; i++) ret[i] = true; for (long i = 2; i * i <= N; i++) if (!ret[i]) continue; else for (long j = i * i; j < ret.Length; j += i) ret[j] = false; return ret; } /// /// Enumerate all the prime numbers in [1,n]. Time complexity: O(N loglog N) /// public static List SieveList(int N) { var res = Sieve(N); var ret = new List(); for (int i = 0; i < res.Length; i++) if (res[i]) ret.Add(i); return ret; } } #endregion