fn main() { let mut io = IO::new(); input!{ from io, t: usize, query: [(i64, i64); t] } for &(x, k) in &query { io.println(solve(x, k)); } } fn solve(x: i64, k: i64) -> i64 { let sigma = 5; const MOD: i64 = 1_000_000_007; let cx = baby_giant(sigma, x, MOD).unwrap(); let k_inv = modinv(k, MOD-1); return modpow(sigma, k_inv * cx, MOD); } pub fn modinv(mut x: i64, modulo: i64) -> i64 { x = x.rem_euclid(modulo); extgcd(x, modulo).0.rem_euclid(modulo) } // return (x, y) s.t. a * x + b * y = gcd(a, b) pub fn extgcd(a: i64, b: i64) -> (i64, i64) { let mut x1 = 1; let mut y1 = 0; let mut m = a; let mut x2 = 0; let mut y2 = 1; let mut n = b; while m % n != 0 { let q = m / n; x1 -= q * x2; y1 -= q * y2; m -= q * n; std::mem::swap(&mut x1, &mut x2); std::mem::swap(&mut y1, &mut y2); std::mem::swap(&mut m, &mut n); } (x2, y2) } pub fn modpow(x: i64, mut y: i64, modulo: i64) -> i64 { let mut ret = 1; let mut cur = x; while y > 0 { if y & 1 > 0 { ret = ret * cur % modulo; } cur = cur * cur % modulo; y >>= 1; } ret } use std::collections::HashMap; pub fn baby_giant(x: i64, y: i64, modulo: i64) -> Option { if (y - 1) % modulo == 0 { return Some(0); } if y == 0 { let (mut lo, mut hi) = (0, modulo); while hi - lo > 1 { let mid = (hi + lo) / 2; if modpow(x, mid, modulo) == 0 { hi = mid; } else { lo = mid; } } return if modpow(x, hi, modulo) == 0 { Some(hi) } else { None }; } let mut dic: HashMap = HashMap::new(); let sq = (modulo as f64).sqrt() as i64 + 1; let mut z = y; for i in 0..sq { // dic[y * x ^ i] = i dic.insert(z, i); z = z * x % modulo; } let r = modpow(x, sq, modulo); // r = x ^ (-sq) let mut c = 1; for i in 1..=sq { c = c * r % modulo; if let Some(v) = dic.get(&c) { let res = i * sq - v; return if modpow(x, res, modulo) == y { Some(res) } else { None }; } } None } // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } pub fn scan(&mut self) -> ::Output { ::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec<::Output> { (0..n).map(|_| self.scan::()).collect() } pub fn print(&mut self, x: T) { ::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { type Output; fn scan(io: &mut IO) -> Self::Output; } macro_rules! impl_scan { ($($t:tt),*) => { $( impl Scan for $t { type Output = Self; fn scan(s: &mut IO) -> Self::Output { s.scan_str().parse().unwrap() } } )* }; } impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String); pub enum Bytes {} impl Scan for Bytes { type Output = &'static [u8]; fn scan(s: &mut IO) -> Self::Output { s.scan_str().as_bytes() } } pub enum Chars {} impl Scan for Chars { type Output = Vec; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().collect() } } pub enum Usize1 {} impl Scan for Usize1 { type Output = usize; fn scan(s: &mut IO) -> Self::Output { s.scan::().wrapping_sub(1) } } impl Scan for (T, U) { type Output = (T::Output, U::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { type Output = (T::Output, U::Output, V::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { type Output = (T::Output, U::Output, V::Output, W::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for String { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } mod neboccoio_macro { #[macro_export] macro_rules! input { (@start $io:tt @read @rest) => {}; (@start $io:tt @read @rest, $($rest: tt)*) => { input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @rest mut $($rest:tt)*) => { input!(@start $io @read @mut [mut] @rest $($rest)*) }; (@start $io:tt @read @rest $($rest:tt)*) => { input!(@start $io @read @mut [] @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:tt] $($rest:tt)*) => { let $($mut)* $var = $io.scan_vec::<$kind>($len); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => { let $($mut)* $var = $io.scan::<$kind>(); input!(@start $io @read @rest $($rest)*) }; (from $io:tt $($rest:tt)*) => { input!(@start $io @read @rest $($rest)*) }; } } // ------------ io module end ------------