use std::io::Write; fn run() { input! { n: usize, q: usize, k: i64, a: [i64; n], ask: [(usize1, usize); q], } let mut prime = (rand() % 2000000000000000000 + 1) as u64; while prime < 10u64.pow(18) || !is_prime_miller(prime as u64) { prime = (rand() % 2000000000000000000 + 1) as u64; } let add = |a: u64, b: u64| -> u64 { let mut c = a + b; if c >= prime { c -= prime; } c }; let sub = |a: u64, b: u64| -> u64 { let mut c = a - b; if a < b { c += prime; } c }; let mul = |mut a: u64, mut b: u64| -> u64 { let mut t = 0; while b > 0 { if b & 1 == 1 { t = add(t, a); } a = add(a, a); b >>= 1; } t }; let r = k as u64 % prime; let mut pow = vec![1; n + 1]; for i in 1..(n + 1) { pow[i] = mul(pow[i - 1], r); } let mut sum = vec![0; n + 1]; for (i, a) in a.iter().enumerate().rev() { let a = ((*a % prime as i64 + prime as i64) % prime as i64) as u64; sum[i] = add(mul(sum[i + 1], r), a); } let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for (l, r) in ask { let val = sub(sum[l], mul(sum[r], pow[r - l])); let ans = if val == 0 { "No" } else { "Yes" }; writeln!(out, "{}", ans).ok(); } } fn main() { run(); } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn rand_memory() -> usize { Box::into_raw(Box::new("I hope this is a random number")) as usize } fn rand() -> usize { static mut X: usize = 0; unsafe { if X == 0 { X = rand_memory(); } X ^= X << 13; X ^= X >> 17; X ^= X << 5; X } } fn shuffle(a: &mut [T]) { for i in 1..a.len() { let p = rand() % (i + 1); a.swap(i, p); } } // ---------- begin miller-rabin ---------- fn is_prime_miller(n: u64) -> bool { if n <= 1 { return false; } else if n <= 3 { return true; } else if n % 2 == 0 { return false; } let pow = |r: u64, mut m: u64| -> u64 { let mut t = 1u128; let mut s = (r % n) as u128; let n = n as u128; while m > 0 { if m & 1 == 1 { t = t * s % n; } s = s * s % n; m >>= 1; } t as u64 }; let mut d = n - 1; let mut s = 0; while d % 2 == 0 { d /= 2; s += 1; } const B: [u64; 7] = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]; for &b in B.iter() { let mut a = pow(b, d); if a <= 1 { continue; } let mut i = 0; while i < s && a != n - 1 { i += 1; a = (a as u128 * a as u128 % n as u128) as u64; } if i >= s { return false; } } true } // ---------- end miller-rabin ----------