Problem:
Score : 900 points

Problem Statement

There are 2N points evenly spaced on the circumference of a circle.
These points are numbered 1 to 2N in clockwise order, starting from some of them.

Snuke will divide these points into N pairs, then for each pair, he will draw a line segment connecting the two points.
After the line segments are drawn, two points are connected when one can reach from one of those points to the other by traveling only on the line segments.
The number of the connected parts here is the number of the connected components in the graph with 2N vertices, corresponding to the 2N points, where every pair of vertices corresponding to two connected points is connected with an edge.

Snuke has already decided K of the pairs, and the i-th of them is a pair of Point A_i and Point B_i.

He is thinking of trying all possible ways to make the remaining N-K pairs and counting the number of the connected parts for each of those ways.
Find the sum of those numbers of the connected parts.
As the answer can be extremely large, compute the sum modulo 10^9+7.

Constraints

1 \leq N \leq 300

0 \leq K \leq N

1 \leq A_i,B_i \leq 2N

A_1,\ A_2,\ ...\ A_K,\ B_1,\ B_2,\ ...\ B_K are all distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 B_1
A_2 B_2
:
A_K B_K

Output

Print the sum of the numbers of the connected parts for all possible ways to make the remaining N-K pairs.

Sample Input 1

2 0

Sample Output 1

5

There are three ways to draw line segments, as shown below, and the number of the connected parts for these ways are 2, 2 and 1, respectively.
Thus, the answer is 2+2+1=5.

Sample Input 2

4 2
5 2
6 1

Sample Output 2

6

Sample Input 3

20 10
10 18
11 17
14 7
4 6
30 28
19 24
29 22
25 32
38 34
36 39

Sample Output 3

27087418

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

//set many funcs template
//Ver.20190820
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#include<assert.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
void swap(int *a,int *b){int c;c=(*a);(*a)=(*b);(*b)=c;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
void llswap(long long *a,long long *b){long long c;c=(*a);(*a)=(*b);(*b)=c;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
void dbswap(double *a,double *b){double c;c=(*a);(*a)=(*b);(*b)=c;}
void chswap(char *a,char *b){char c;c=(*a);(*a)=(*b);(*b)=c;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

void getperm(int a[],int n){
  int i,p;
  for(i=0;i<n;i++){
    a[i]=i;
  }
  for(i=n-1;i>=1;i--){
    p=rand()%(i+1);
    swap(&a[p],&a[i]);
  }
}

typedef struct{
int val;
int node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
return 0;
}

void coordinate_comp(int a[],int n){
  int i,c=0;
  sd dat[524288];
  for(i=0;i<n;i++){
    dat[i].val=a[i];
    dat[i].node=i;
  }
  qsort(dat,n,sizeof(dat[0]),sdsortfnc);
  a[dat[0].node]=c;
  for(i=1;i<n;i++){
    if(dat[i-1].val!=dat[i].val){c++;}
    a[dat[i].node]=c;
  }
}

long long ssize=1024;
long long stree[2][2048];
long long vd[2];

void sinit(){
    long long i;
    vd[0]=llinf;
    vd[1]=-llinf;
    for(i=0;i<2*ssize;i++){
        stree[0][i]=llinf;
        stree[1][i]=-llinf;
    }
}

void upd(long long k,long long a){
    k+=ssize-1;
    stree[0][k]=a;
    stree[1][k]=a;
    while(k>0){
        k=(k-1)/2;
        stree[0][k]=llmin(stree[0][2*k+1],stree[0][2*k+2]);
        stree[1][k]=llmax(stree[1][2*k+1],stree[1][2*k+2]);
    }
}

//calc min[a,b)(t=0)
//calc max[a,b)(t=1)
//call:k=0,l=0,r=ssize
long long query(long long a,long long b,long long t,long long k,long long l,long long r){
    long long ld,rd;
    if(r<=a || b<=l){
      return vd[t];
    }
    if(a<=l && r<=b){
        return stree[t][k];
    }
    else{
        ld=query(a,b,t,k*2+1,l,(l+r)/2);
        rd=query(a,b,t,k*2+2,(l+r)/2,r);
        if(t==0){return llmin(ld,rd);}
        else{return llmax(ld,rd);}
    }
}

//Binary Indexed Tree
long long bit[1116]={0},bsize=1024;
long long sum(long long i){
    long long s=0;
    while(i>0){
        s+=bit[i];
        i-=i&(-i);
    }
    return s;
}
void add(long long i,long long x){
    while(i<=bsize){
        bit[i]+=x;
        i+=i&(-i);
    }
}

long long dp[666][666];
long long pat[666]={0};
long long pr[666]={0};

long long rep(long long l,long long r){
  if(r-l<=0){return 0;}
  if(dp[l][r]!=-1){return dp[l][r];}
  long long i,c;
  if(query(l,r+1,0,0,0,ssize)<l){return 0;}
  if(query(l,r+1,1,0,0,ssize)>r){return 0;}
  if(l+1==r){return 1;}
  dp[l][r]=0;
  c=sum(r)-sum(l-1);
  if(c%2==0){
    dp[l][r]=pat[c];
    for(i=l;i<r;i++){
      if(pr[i]==0){c--;}
      if/*(c%2==1)*/(c&1ll){continue;}
      dp[l][r]=(dp[l][r]+mod-((rep(l,i)*pat[c])%mod))%mod;
    }
  }
  return dp[l][r];
}

int main(void){
  sinit();
  long long i,j,n,k,a,b,r=0;
  scanf("%lld%lld",&n,&k);
  pat[0]=1;
  pat[1]=0;
  for(i=2;i<666;i++){
    pat[i]=(pat[i-2]*(i-1))%mod;
  }
  for(i=1;i<=2*n;i++){add(i,1);}
  for(i=0;i<k;i++){
    scanf("%lld%lld",&a,&b);
    pr[a]=b;
    pr[b]=a;
    upd(a,b);
    upd(b,a);
    add(a,-1);
    add(b,-1);
  }
  for(i=0;i<666;i++){
    for(j=0;j<666;j++){
      dp[i][j]=-1;
    }
  }
  for(i=1;i<=2*n;i++){
    for(j=i+1;j<=2*n;j++){
      //printf("%lld %lld : %lld\n",i,j,rep(i,j));
      r=(r+rep(i,j)*pat[2*(n-k)-(sum(j)-sum(i-1))])%mod;
    }
  }
  printf("%lld\n",r);
  return 0;
}