【多項式】拉格朗日插值

洛谷 - P4781 【模闆】拉格朗日插值

// Luogu P4781 拉格朗日插值
#include <bits/stdc++.h>
#define ll long long
#define N 2003
#define MOD 998244353ll
using namespace std;
int n;
ll k, x[N], y[N];
ll ans = 0ll;
ll qpow(ll a, ll b, ll p = MOD) {
    ll res = 1;
    a %= p;
    for (; b; b >>= 1, a = a * a % p) {
        if (b & 1) {
            res = res * a % p;
        }
    }
    return (res + p) % p;
}
ll inv(ll a, ll p = MOD) { return qpow(a, p - 2); }
int main() {
    scanf("%d%lld", &n, &k);
    for (int i = 1; i <= n; ++i) {
        scanf("%lld%lld", &x[i], &y[i]);
    }
    for (int i = 1; i <= n; ++i) {
        ll s1 = y[i];
        ll s2 = 1ll;
        for (int j = 1; j <= n; ++j) {
            if (i == j) continue;
            s1 = s1 * (k - x[j]) % MOD;
            s2 = s2 * (x[i] - x[j]) % MOD;
        }
        ans += s1 * inv(s2) % MOD;
    }
    printf("%lld\n", (ans % MOD + MOD) % MOD);
    return 0;
}