题解

#include<bits/stdc++.h>
#define rep(i, a, b) for (int i = (a); i <= int(b); i++)
#define per(i, a, b) for (int i = (a); i >= int(b); i--)
using namespace std;
typedef long long ll;
const int maxn = 5e5, mod = 1e9 + 7;
int n, k, w[10], c[maxn + 5], d[maxn + 5], dt[10], res, S[11][11], inv[12];
struct foo {
int z[10], l[10], r[10];
void reset() {
memset(z, 0, k << 2);
memset(l, 0, k << 2);
memset(r, 0, k << 2);
}
foo() {
reset();
}
int walk(int c, int d) {
z[c] += d;
if (z[c] < l[c] || z[c] > r[c]) {
l[c] = min(l[c], z[c]);
r[c] = max(r[c], z[c]);
return d;
}
return 0;
}
} F, B;
inline void red(int &x) {
x += x >> 31 & mod;
}
void prework(int n) {
S[0][0] = 1;
rep(i, 1, n) rep(j, 1, i) {
S[i][j] = (S[i - 1][j - 1] + ll(S[i - 1][j]) * j) % mod;
}
inv[1] = 1;
rep(i, 2, n + 1) {
inv[i] = ll(mod - mod / i) * inv[mod % i] % mod;
}
}
int calc(int k, int n) {
int s = 0, c = 1;
rep(i, 0, k) {
c = ll(c) * max(0, n - i) % mod;
s = (s + ll(c) * inv[i + 1] % mod * S[k][i]) % mod;
}
return s;
}
int work(int a[]) {
int lim = mod;
rep(i, 0, k - 1) if (dt[i]) {
lim = min(lim, (a[i] + dt[i] - 1) / dt[i]);
}
int dp[11] = { 1 };
rep(i, 0, k - 1) {
per(j, i, 0) {
dp[j + 1] = (dp[j + 1] + ll(mod - dt[i]) * dp[j]) % mod;
dp[j] = ll(a[i]) * dp[j] % mod;
}
}
int res = 0;
rep(i, 0, k) {
res = (res + ll(dp[i]) * calc(i, lim)) % mod;
}
return res;
}
int main() {
scanf("%d %d", &n, &k);
prework(k);
rep(i, 0, k - 1) {
scanf("%d", &w[i]);
}
rep(i, 1, n) {
scanf("%d %d", &c[i], &d[i]), c[i]--;
if (F.walk(c[i], d[i]) && F.r[c[i]] - F.l[c[i]] <= w[c[i]]) {
int x = 1;
rep(j, 0, k - 1) if (j != c[i]) {
x = ll(x) * max(0, w[j] - F.r[j] + F.l[j]) % mod;
}
res = (res + ll(i) * x) % mod;
}
}
rep(i, 1, n) if (F.z[c[i]] < 0) {
d[i] = -d[i];
}
rep(i, 0, k - 1) if (F.z[i] < 0) {
F.z[i] = -F.z[i];
swap(F.l[i], F.r[i]);
F.l[i] = -F.l[i];
F.r[i] = -F.r[i];
}
B = F;
bool chk = true;
rep(i, 0, k - 1) {
dt[i] = B.z[i];
chk &= dt[i] == 0;
}
if (chk) {
bool ok = false;
rep(i, 0, k - 1) {
ok |= B.r[i] - B.l[i] >= w[i];
}
printf("%d\n", ok ? res : -1);
exit(0);
}
int a[10] = {};
rep(i, 1, n) {
if (F.walk(c[i], d[i]) && F.r[c[i]] - F.l[c[i]] <= w[c[i]]) {
bool ok = true;
rep(j, 0, k - 1) if (j != c[i]) {
ok &= w[j] - F.r[j] + F.l[j] > 0;
}
if (!ok) {
continue;
}
rep(j, 0, k - 1) if (j != c[i]) {
a[j] = w[j] - F.r[j] + F.l[j];
}
a[c[i]] = w[c[i]] - F.r[c[i]] + F.l[c[i]] + 1, res = (res + ll(i) * work(a)) % mod;
a[c[i]] = w[c[i]] - F.r[c[i]] + F.l[c[i]], res = (res + ll(mod - i) * work(a)) % mod;
}
}
rep(i, 0, k - 1) {
a[i] = max(0, w[i] - B.r[i] + B.l[i]);
}
res = (res + ll(n) * work(a)) % mod;
printf("%d\n", res);
return 0;
}