This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*input
2
1 2
2 3
*/
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdio>
using namespace std;
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define FORA(i, a) for (auto &i : a)
#define FORB(i, a, b) for (int i = a; i >= b; --i)
const int MOD = 1000000007, MAXN = 507;
int add(int x, int y) { return x -= ((x += y) >= MOD ? MOD : 0); }
int sub(int x, int y) { return x += ((x -= y) < 0 ? MOD : 0); }
int mul(int x, int y) { return (int) ((long long) x * y % MOD); }
int getinv(int x, int m) { return (x == 1 ? 1 : m - (int) ((long long) m * getinv(m % x, x) / x)); }
int N, A[MAXN], B[MAXN], M;
int eval[MAXN * 2][MAXN], inv[MAXN], prefsum[MAXN * 2];
vector<int> vals, dp[MAXN * 2];
void addfunc(vector<int> &a, vector<int> b)
{
a.resize(max(a.size(), b.size()));
FOR(i, 0, int(min(a.size(), b.size())) - 1) a[i] = add(a[i], b[i]);
}
int evalat(vector<int> &a, int x)
{
int ans = 0;
FOR(i, 0, ((int) a.size()) - 1) ans = add(ans, mul(eval[x][i], a[i]));
return ans;
}
vector<int> sumfunc(vector<int> &a)
{
if (a.empty()) return a;
vector<int> b = a;
b.insert(b.begin(), 0);
return b;
}
void addint(vector<int> &a, int x)
{
if (not a.empty()) a[0] = add(a[0], x);
else a.push_back(x);
}
void subint(vector<int> &a, int x)
{
if (not a.empty()) a[0] = sub(a[0], x);
else a.push_back(x ? MOD - x : x);
}
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> N;
FOR(i, 1, N) {
cin >> A[i] >> B[i];
--A[i];
vals.push_back(A[i]);
vals.push_back(B[i]);
}
vals.push_back(-1);
sort(vals.begin(), vals.end());
vals.erase(unique(vals.begin(), vals.end()), vals.end());
FOR(i, 1, N) {
A[i] = (int) (lower_bound(vals.begin(), vals.end(), A[i]) - vals.begin());
B[i] = (int) (lower_bound(vals.begin(), vals.end(), B[i]) - vals.begin());
}
FOR(i, 1, N + 5) inv[i] = getinv(i, MOD);
M = (int) vals.size() - 1;
FOR(i, 1, M) {
eval[i][0] = 1;
FOR(j, 1, N + 5) eval[i][j] = mul(eval[i][j - 1], mul((vals[i] + j - 1) % MOD, inv[j]));
// FOR(j, 1, N + 5) cout << vals[i] << ' ' << j << ": " << eval[i][j] << endl;
}
FOR(id, 1, N) {
int l = A[id], r = B[id];
// cout << l << ' ' << r << " - " << vals[l] << ' ' << vals[r] << endl;
FOR(i, 1, r - 2) {
vector<int> sumf = sumfunc(dp[i]);
int cur = sub(evalat(sumf, i + 1), evalat(sumf, i));
prefsum[i] = add(prefsum[i - 1], cur);
// cout << vals[i] << ' ' << vals[i + 1] << ": " << cur << ' ' << dp[i].size() << endl;
}
// cout << "S" << endl;
FORB(i, r - 1, l) {
// cout << vals[i] << ' ' << vals[i + 1] << ": " << dp[i].size();
vector<int> sumf = sumfunc(dp[i]);
vector<int> vec = sumf;
addint(vec, prefsum[i - 1]);
subint(vec, evalat(sumf, i));
addint(vec, 1);
dp[i] = move(vec);
// cout << " " << dp[i].size() << endl;
}
}
// cout << " - " << endl;
FOR(i, 1, M - 1) {
vector<int> sumf = sumfunc(dp[i]);
int cur = sub(evalat(sumf, i + 1), evalat(sumf, i));
prefsum[i] = add(prefsum[i - 1], cur);
// cout << vals[i] << ' ' << vals[i + 1] << ": " << cur << ' ' << dp[i].size() << endl;
}
cout << prefsum[M - 1] << endl;
}
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