10484: ABC104 —— C - All Green
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Description
A programming competition site _AtCode_ provides algorithmic problems. Each problem is allocated a score based on its difficulty. Currently, for each integer $i$ between $1$ and $D$ (inclusive), there are $p_i$ problems with a score of $100i$ points. These $p_1 + … + p_D$ problems are all of the problems available on AtCode.
A user of AtCode has a value called _total score_. The total score of a user is the sum of the following two elements:
- Base score: the sum of the scores of all problems solved by the user.
- Perfect bonuses: when a user solves all problems with a score of $100i$ points, he/she earns the perfect bonus of $c_i$ points, aside from the base score $(1 ≤ i ≤ D)$.
Takahashi, who is the new user of AtCode, has not solved any problem. His objective is to have a total score of $G$ or more points. At least how many problems does he need to solve for this objective?
A user of AtCode has a value called _total score_. The total score of a user is the sum of the following two elements:
- Base score: the sum of the scores of all problems solved by the user.
- Perfect bonuses: when a user solves all problems with a score of $100i$ points, he/she earns the perfect bonus of $c_i$ points, aside from the base score $(1 ≤ i ≤ D)$.
Takahashi, who is the new user of AtCode, has not solved any problem. His ob
Input
Input is given from Standard Input in the following format:
```
$D$ $G$
$p_1$ $c_1$
$:$
$p_D$ $c_D$
```
```
$D$ $G$
$p_1$ $c_1$
$:$
$p_D$ $c_D$
```
Output
Print the minimum number of problems that needs to be solved in order to have a total score of $G$ or more points. Note that this objective is always achievable (see Constraints).
Constraints
- $1 ≤ D ≤ 10$
- $1 ≤ p_i ≤ 100$
- $100 ≤ c_i ≤ 10^6$
- $100 ≤ G$
- All values in input are integers.
- $c_i$ and $G$ are all multiples of $100$.
- It is possible to have a total score of $G$ or more points.
- $1 ≤ p_i ≤ 100$
- $100 ≤ c_i ≤ 10^6$
- $100 ≤ G$
- All values in input are integers.
- $c_i$ and $G$ are all multiples of $100$.
- It is possible to have a total score of $G$ or more points.
Sample 1 Input
2 700
3 500
5 800
Sample 1 Output
3
In this case, there are three problems each with 100 points and five problems each with 200 points. The perfect bonus for solving all the 100100-point problems is 500 points, and the perfect bonus for solving all the 200-point problems is 800 points. Takahashi's objective is to have a total score of 700 points or more.
One way to achieve this objective is to solve four 200-point problems and earn a base score of 800 points. However, if we solve three 100-point problems, we can earn the perfect bonus of 500 points in addition to the base score of 300 points, for a total score of 800 points, and we can achieve the objective with fewer problems.
Sample 2 Input
2 2000
3 500
5 800
Sample 2 Output
7
This case is similar to Sample Input 1, but the Takahashi's objective this time is 2000 points or more. In this case, we inevitably need to solve all five 200-point problems, and by solving two 100-point problems additionally we have the total score of 2000 points.
Sample 3 Input
2 400
3 500
5 800
Sample 3 Output
2
This case is again similar to Sample Input 1, but the Takahashi's objective this time is 400 points or more. In this case, we only need to solve two 200-point problems to achieve the objective.
5 25000
20 1000
40 1000
50 1000
30 1000
1 1000
66
There is only one 500-point problem, but the perfect bonus can be earned even in such a case.