Hungry Cow

Note: The time limit for this problem is 6s, three times the default. The memory limit for this problem is 512MB, twice the default.

Bessie is a hungry cow. Each day, for dinner, if there is a haybale in the barn, she will eat one haybale. Farmer John does not want Bessie to starve, so some days he sends a delivery of haybales, which arrive in the morning (before dinner). In particular, on day $d_i$, Farmer John sends a delivery of $b_i$ haybales ($1\leq d_i \leq 10^{14}$, $0\leq b_i \leq 10^9$).

Process $U$ ($1\le U\le 10^5$) updates as follows: Given a pair $(d, b)$, update the number of haybales arriving on day $d$ to $b$. After each update, output the sum of all days on which Bessie eats haybales modulo $10^9+7$.

$U$, followed by $U$ lines containing the updates.

• Input 3: $U\le 5000$
• Inputs 4-10: Updates only increase the number of haybales arriving on day $d$.
• Inputs 11-22: No additional constraints.

The sum after each update modulo $10^9+7$.

Answers after each update: