NOIP T1正确性求证明

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 1;
ll m;
int n;
struct node
{
    ll x, y;
}a[N];
bool cmp(node x, node y)
{
    return x.x + x.y < y.x + y.y;
}
bool cmp2(node x, node y)
{
    return x.x < y.x;
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
//	freopen("candy.in", "r", stdin);
//	freopen("candy.out", "w", stdout);
	cin >> n >> m;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i].x >> a[i].y;
    }
    sort(a + 1, a + n + 1, cmp);
    sort(a + 2, a + n + 1, cmp2);
    ll cnt = a[1].x + a[1].y, ans = m / cnt * 2 + (m % cnt >= a[1].x);
    ll sum = 0;
    for(int i = 2; i <= n; i++)
    {
        sum += a[i].x;
        if(sum > m) break;
        ans = max(ans, i - 1 + (m - sum) / cnt * 2 + ((m - sum) % cnt >= a[1].x));
    }
    cout << ans;
    return 0;
}