write a go solution for Description:
Divan's new cottage is finally complete! However, after a thorough inspection, it turned out that the workers had installed the insulation incorrectly, and now the temperature in the house directly depends on the temperature outside. More precisely, if the temperature in the house is P in the morning, and the street temperature is T, then by the next morning the temperature in the house changes according to the following rule:

- P_new=P+1, if P<T,
- P_new=P-1, if P>T,
- P_new=P, if P=T.

Divan is a very busy businessman, so sometimes he is not at home for long periods and does not know what the temperature is there now, so he hired you to find it. You will work for n days. In the beginning of the i-th day, the temperature outside T_i is first given to you. After that, on the i-th day, you will receive k_i queries. Each query asks the following: "if the temperature in the house was x_i at the morning of the first day, what would be the temperature in the house next morning (after day i)?"

Please answer all the businessman's queries.

Input Format:
The first line of the input contains the number n (1<=n<=2*10^5) — the number of days.

The following is a description of n days in the following format.

The first line of the description contains an integer T_i (0<=T_i<=10^9) — the temperature on that day.

The second line contains a non-negative integer k_i (0<=k_i<=2*10^5) — the number of queries that day.

The third line contains k integers x'_i (0<=x'_i<=10^9) — the encrypted version of Divan's queries.

Let lastans=0 initially. Divan's actual queries are given by x_i=(x'_i+lastans)bmod(10^9+1), where abmodb is the reminder when a is divided by b. After answering the query, set lastans to the answer.

It is guaranteed that the total number of queries (the sum of all k_i) does not exceed 2*10^5.

Output Format:
For each query, output a single integer — the temperature in the house after day i.

Note:
Let's look at the first four queries from the example input.

The temperature is 50 on the first day, 50 on the second day, and 0 on the third day.

Note that lastans=0 initially.

- The initial temperature of the first query of the first day is (1,+,lastans)bmod(10^9+1)=1. After the first day, the temperature rises by 1, because 1<50. So the answer to the query is 2. Then, we set lastans=2.
- The initial temperature of the second query of the first day is (2,+,lastans)bmod(10^9+1)=4. After the first day, the temperature rises by 1, because 4<50. So the answer to the query is 5. Then, we set lastans=5.
- The initial temperature of the third query of the first day is (3,+,lastans)bmod(10^9+1)=8. After the first day, the temperature rises by 1. So the answer to the query is 9. Then, we set lastans=9.
- The initial temperature of the first query of the second day is (4,+,lastans)bmod(10^9+1)=13. After the first day, the temperature rises by 1. After the second day, the temperature rises by 1. So the answer to the query is 15. Then, we set lastans=15.. Output only the code with no comments, explanation, or additional text.