C. Tourist's Notes

C. Tourist's Notes

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer hi. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all i's from 1 to n - 1 the inequality |hi - hi + 1| ≤ 1 holds.

At the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |hi - hi + 1| ≤ 1.

Input

The first line contains two space-separated numbers, n and m (1 ≤ n ≤ 108, 1 ≤ m ≤ 105) — the number of days of the hike and the number of notes left in the journal.

Next m lines contain two space-separated integers di and hdi (1 ≤ di ≤ n, 0 ≤ hdi ≤ 108) — the number of the day when the i-th note was made and height on the di-th day. It is guaranteed that the notes are given in the chronological order, i.e. for all i from 1 to m - 1 the following condition holds: di < di + 1.

Output

If the notes aren't contradictory, print a single integer — the maximum possible height value throughout the whole route.

If the notes do not correspond to any set of heights, print a single word 'IMPOSSIBLE' (without the quotes).

Examples

input

8 2
2 0
7 0

output

2

input

8 3
2 0
7 0
8 3

output

IMPOSSIBLE

Note

For the first sample, an example of a correct height sequence with a maximum of 2: (0, 0, 1, 2, 1, 1, 0, 1).

In the second sample the inequality between h7 and h8 does not hold, thus the information is inconsistent.

思路：二分；

分别讨论第一个点前后最后一个点后，贪心选取最大，然后再二分每两个点之间能取得的最大值，当两个点的差大于两点间的距离时无解，复杂度（n*log（n））；

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<queue>
 4 #include<stdlib.h>
 5 #include<stack>
 6 #include<stdio.h>
 7 #include<string.h>
 8 using namespace std;
 9 typedef struct node
10 {
11     int day;
12     int hi;
13 } ss;
14 ss ans[1000005];
15 int main(void)
16 {
17     int n,m;
18     while(scanf("%d %d",&n,&m)!=EOF)
19     {
20         int i,j;
21         int flag = 0;
22         for(i = 0; i < m; i++)
23             scanf("%d %d",&ans[i].day,&ans[i].hi);
24         int maxx = -1;
25         for(i = 0; i < m; i++)
26         {
27             if(i == 0)
28             {
29                 maxx = max(ans[i].day-1+ans[i].hi,maxx);
30             }
31             else
32             {
33                 if(abs(ans[i].hi-ans[i-1].hi)>ans[i].day-ans[i-1].day)
34                     flag = 1;
35                 else
36                 {
37                     int l = max(ans[i-1].hi,ans[i].hi);
38                     int r = 1e9;
39                     while(l<=r)
40                     {
41                         int mid = (l+r)/2;
42                         int x = abs(mid-ans[i].hi);
43                         int y = abs(mid-ans[i-1].hi);//printf("%d\n",mid);
44                         if(x+y<=ans[i].day-ans[i-1].day)
45                         {
46                             maxx = max(maxx,mid);
47                             l = mid+1;
48                         }
49                         else r = mid-1;
50                     }
51                 }
52             } if(i == m-1)
53             {
54                 maxx = max(maxx,n-ans[i].day+ans[i].hi);
55             }
56         }if(flag)printf("IMPOSSIBLE\n");
57         else
58         printf("%d\n",maxx);
59     }
60     return 0;
61 }

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