404697: GYM101611 H Hilarious Cooking

All laws of physics appearing in this problem statement are fictitious. Any resemblance to the real world is purely coincidental.

To discuss problem proposals and select a proper problemset for an upcoming competition jury team has gathered at a magnificent palace in Moscow suburbs (typically called dacha). Chief judge is now struggling to prepare a roast beef barbecue using a recipe he just found in the Internet.

According to recipe a roast beef should be cooked for exactly n seconds. The total amount of heat received by beef should be equal to T. Formally, if we denote the temperature inside the barbecue during the i-th second as t_i, the sum t₁ + t₂ + ... + t_n should be equal to T. Moreover, there are m additional instructions, the i-th of them states that in order to achieve the perfect result the temperature inside the barbecue during the a_i-th second should be equal to b_i, i.e. t_ai should be b_i.

However, the task is complicated by the fact that the barbecue that chief judge is using this time has some restrictions. First of all, the barbecue only allows t_i to take non-negative integer values. Second, t_i can't change too fast, i.e. the condition |t_i - t_i + 1| ≤ 1 should be satisfied for all i from 1 to n - 1.

There are no other restrictions, in particular it is allowed to start and finish with any temperature, i.e. the values t₁ and t_n can be arbitrary non-negative integers, unless the opposite is directly specified in the recipe. Your goal is to help chief judge and determine whether his task is even possible, or he should look for another recipe.

The first line of the input contains three integers T, n and m (1 ≤ T ≤ 10¹⁸, 1 ≤ n ≤ 2·10⁹, 1 ≤ m ≤ 100 000) — the total amount of heat that beef should receive, the exact number of seconds it should be cooked for, and the number of instructions in the recipe.

The next m lines contain the instructions in chronological order. The i-th instruction is defined by two integers a_i and b_i (1 ≤ a_i ≤ n, 0 ≤ b_i ≤ 10⁹) stating that the temperature inside the barbecue should be equal to b_i during the second a_i. It is guaranteed that a₁ < a₂ < ... < a_m.

If there exists a sequence of non-negative t₁, t₂, ..., t_n such that , |t_i - t_i + 1| ≤ 1 for all 1 ≤ i ≤ n - 1, and t_ai = b_i for all i from 1 to m, print "Yes" (without quotes) in the only line of the output. Otherwise, print "No" (without quotes).

3 3 1
2 1

Yes

10 3 1
1 1

No

13 5 2
2 2
4 2

Yes

In the first sample, a possible solution is t₁ = t₂ = t₃ = 1. In the third sample, a possible solution is t₁ = 3, t₂ = 2, t₃ = 3, t₄ = 2, t₅ = 3.