pub(crate) fn extended_euclid(f: i64, g: i64) -> (usize, Vec<i64>, Vec<i64>, Vec<i64>, Vec<i64>) {
let mut s: Vec<i64> = vec![1, 0];
let mut t: Vec<i64> = vec![0, 1];
let mut r: Vec<i64> = vec![f, g];
let mut q: Vec<i64> = vec![0];
let mut i = 1;
while r[i] != 0 {
q.push(r[i - 1] / r[i]); r.push(r[i - 1] - q[i] * r[i]); s.push(s[i - 1] - q[i] * s[i]); t.push(t[i - 1] - q[i] * t[i]); i += 1;
}
let l: usize = i - 1;
(l, r, s, t, q)
}
pub(crate) fn i_crt(modulus: &[u64], val: &[u64]) -> u64 {
let big_mod = modulus.iter().product::<u64>();
let mut c: Vec<u64> = vec![0; val.len()];
let mut out: u64 = 0;
for i in 0..val.len() {
let tmp_mod = big_mod / modulus[i];
let (l, _, s, _, _) = extended_euclid(tmp_mod as i64, modulus[i] as i64);
let sl: u64 = if s[l] < 0 {
(s[l] % modulus[i] as i64 + modulus[i] as i64) as u64
} else {
s[l] as u64
};
c[i] = val[i].wrapping_mul(sl);
c[i] %= modulus[i];
out = out.wrapping_add(c[i] * tmp_mod);
}
out % big_mod
}