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#include <iostream>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <vector>
using namespace std;
const int gox[5]={1,0,-1,0,0},goy[5]={0,1,0,-1,0};
const int mo=1e9+7;
int sign;
int check(int k1,int k2,int k3,int k4){
	for (int i=0;i<4;i++)
		if (k3==k1+gox[i]&&k4==k2+goy[i]) return 1;
	return 0;
}
struct pattern{
	int A[8],B[8];
	int n,m,len,pd[16],del[8],a[100],b[100],tot;
	void print(){
		cout<<"asd"<<endl;
		int bo[10][10];
		for (int i=1;i<=n;i++)
			for (int j=1;j<=m;j++) bo[i][j]=0;
		for (int i=1;i<=len;i++) bo[A[i]][B[i]]=1;
		for (int i=1;i<=n;i++){
			for (int j=1;j<=m;j++) printf("%d",bo[i][j]);
			putchar('\n');
		}
		//for (int i=1;i<=len;i++) cout<<A[i]<<" "<<B[i]<<endl;
	}
	void init(){
		for (int i=1;i<=len;i++){
			del[i]=0;
			for (int j=1;j<=len;j++)
				if (i!=j) del[i]+=check(A[i],B[i],A[j],B[j]);
		}
		tot=0;
		for (int i=1;i<=len;i++)
			for (int j=0;j<5;j++){
				int aa=A[i]+gox[j],bb=B[i]+goy[j],flag=0;
				for (int k=1;k<=tot;k++)
					if (a[k]==aa&&b[k]==bb){
						flag=1; break;
					}
				if (flag==0){
					tot++; a[tot]=aa; b[tot]=bb;
				}
			}
		if (len!=4){
			for (int i=0;i<(1<<len);i++) pd[i]=1; pd[0]=0;
			return;
		}
		memset(pd,0x00,sizeof pd);
		for (int i=1;i<=4;i++)
			for (int j=i+1;j<=4;j++){
				int flag=0;
				int where1=1; while (where1==i||where1==j) where1++;
				int where2=len; while (where2==i||where2==j) where2--;
				if ((check(A[i],B[i],A[where1],B[where1])&&check(A[j],B[j],A[where2],B[where2]))){
					pd[(1<<i-1)+(1<<j-1)]++; 
				}
				swap(where1,where2);
				if ((check(A[i],B[i],A[where1],B[where1])&&check(A[j],B[j],A[where2],B[where2]))){
					pd[(1<<i-1)+(1<<j-1)]++; 
				}
			}
		for (int i=1;i<(1<<len);i++) pd[i]=1-pd[i];
	//	print();
	//	for (int i=0;i<16;i++) if (pd[i]) cout<<i<<" "; cout<<endl;
	}
};
vector<pattern>x[5];
int K,n,A[10][2];
char ch[3100];
char pd[3100][3100],imp[3100][3100];
int qua(int k1,int k2){
	return k1>0&&k1<=n&&k2>0&&k2<=n;
}
void dfs(int k1,int k2){
	pd[k1][k2]=2;
	for (int i=0;i<4;i++){
		int a=k1+gox[i],b=k2+goy[i];
		if (qua(a,b)&&pd[a][b]==1) dfs(a,b);
	}
}
void check(){
	int flag=0;
	for (int i=1;i<=n;i++) flag|=pd[1][i];
	if (flag==0) return;
	flag=0;
	for (int i=1;i<=n;i++) flag|=pd[i][1];
	if (flag==0) return;
	flag=0;
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (pd[i][j]==1){
				dfs(i,j); flag++;
			}
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (pd[i][j]) pd[i][j]=1;
	if (flag==1){
		pattern k1; k1.len=K;
		for (int i=1;i<=K;i++) k1.A[i]=A[i][0],k1.B[i]=A[i][1];
		k1.n=0; k1.m=0;
		for (int i=1;i<=K;i++) k1.n=max(k1.n,A[i][0]),k1.m=max(k1.m,A[i][1]);
		k1.init();
		x[K].push_back(k1); 
	}
}
void dfs(int k1,int k2,int k3){
	if (k3>n){
		k3=1; k2++;
	}
	if (k2>n){
		if (k1==K+1) check(); return;
	}
	dfs(k1,k2,k3+1); 
	if (k1>K) return;
	pd[k2][k3]=1;
	A[k1][0]=k2; A[k1][1]=k3;
	dfs(k1+1,k2,k3+1); pd[k2][k3]=0;
}
void getpattern(int _K){
	K=_K; n=_K;
	dfs(1,1,1);
}
int impnum,ans;
int quick(int k1,int k2){
	int k3=1;
	while (k2){
		if (k2&1) k3=1ll*k3*k1%mo;
		k2>>=1; k1=1ll*k1*k1%mo;
	}
	return k3;
}
int allimp(){
	int ans=1;
	for (int i=1;i<=K;i++) ans=1ll*ans*(impnum-i+1)%mo;
	for (int i=1;i<=K;i++) ans=1ll*ans*quick(i,mo-2)%mo;
	return ans;
}
int matchpattern(pattern& K){
	int ans=0; //K.print();
	for (int i=0;i<=n-K.n;i++)
		for (int j=0;j<=n-K.m;j++){
			int bo=1,flag=1,ti=0;
			for (int k=1;k<=K.len;k++){
				int a=K.A[k]+i,b=K.B[k]+j;
				flag&=pd[a][b];
				bo&=imp[a][b];
				ti|=(imp[a][b]<<k-1);
			}
		//	cout<<ti<<" "<<K.pd[ti]<<endl;
			if (bo==0&&flag){
				ans+=K.pd[ti];
			//	cout<<"find "<<i<<" "<<j<<endl;
			}
		}
	return ans;
}
char w1[3100][3100],w2[3100][3100];
int del(int k1,int k2){
	int ans=0; //cout<<"del "<<k1<<" "<<k2<<endl;
	if (imp[k1][k2]==0){
		ans--;
		for (int i=0;i<4;i++){
			int a=k1+gox[i],b=k2+goy[i];
			if (imp[a][b]) ans++;
		}
	} else if (imp[k1][k2]){
		for (int i=0;i<4;i++){
			int a=k1+gox[i],b=k2+goy[i];
			if (imp[a][b]^pd[a][b]) ans++;
		}
	}
	return ans;
}
void getw1(){
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++) w1[i][j]=del(i,j);
}
int getwround(int a,int b){
	int ans=0;
	for (int kk=0;kk<5;kk++){
		int aa=a+gox[kk],bb=b+goy[kk];
		if (imp[aa][bb]) ans++;
	}
	return ans;
}
void getw2(){
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++) w2[i][j]=getwround(i,j);
}
int matchwithonepoint(pattern& K){
//	K.print(); 
	long long ans=0;
	for (int i=0;i<=n-K.n;i++)
		for (int j=0;j<=n-K.m;j++){
			int bo=1,flag=1,ti=0;
			for (int k=1;k<=K.len;k++){
				int a=K.A[k]+i,b=K.B[k]+j;
				flag&=pd[a][b];
				bo&=imp[a][b];
				ti|=imp[a][b];
			}
//cout<<i<<" "<<j<<" "<<flag<<" "<<bo<<endl;
			if (bo||flag==0||ti==0) continue;
			//cout<<"asd "<<i<<" "<<j<<endl;
			int nowpoint=0; 
			for (int k=1;k<=K.tot;k++){
				int a=K.a[k]+i,b=K.b[k]+j;
				nowpoint+=imp[a][b];
			}
		//	cout<<"fa "<<nowpoint<<" "<<impnum<<endl;
			ans=(ans+impnum-nowpoint);
		}
	return ans%mo;
}
int matchwithtwopoint(pattern& K){
//	K.print(); 
	int ans=0;
	for (int i=0;i<=n-K.n;i++)
		for (int j=0;j<=n-K.m;j++){
			int bo=1,flag=1,ti=0;
			for (int k=1;k<=K.len;k++){
				int a=K.A[k]+i,b=K.B[k]+j;
				flag&=pd[a][b];
				bo&=imp[a][b];
				ti|=imp[a][b];
			}
//cout<<i<<" "<<j<<" "<<flag<<" "<<bo<<endl;
			if (bo||flag==0||ti==0) continue;
//			cout<<"asd "<<i<<" "<<j<<endl;
			int nowpoint=0;
			for (int k=1;k<=K.len;k++){
				int a=K.A[k]+i,b=K.B[k]+j;
				nowpoint+=w2[a][b];
				if (imp[a][b]) nowpoint-=K.del[k];
			}
			int rem=impnum-nowpoint;
			ans=(ans+1ll*rem*(rem-1)/2)%mo;
		}
	return ans;
}
int matchtwonotimp(){
	int totnum=0; 
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (imp[i][j]==0&&pd[i][j])
				for (int k=0;k<4;k++){
					int a=i+gox[k],b=j+goy[k];
					if (imp[a][b]) totnum++;
				}
	long long ans=0;
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (imp[i][j]==0&&pd[i][j])
				for (int k=0;k<4;k++){
					int a=i+gox[k],b=j+goy[k];
					if (imp[a][b]){
						sign++; 
						int num=w1[i][j]+w1[a][b];
						ans+=totnum-num;
					}
				}
	return ans/2%mo;
}
int main(){
	for (int i=1;i<=4;i++) getpattern(i);
	scanf("%d%d",&n,&K);
	//n=3000;
	for (int i=1;i<=n;i++){
		scanf("%s",ch+1);
		for (int j=1;j<=n;j++){
			pd[i][j]=(rand()%1000==0);
			pd[i][j]=(ch[j]=='.');
		}
	}
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (pd[i][j]==0)
				for (int k=0;k<4;k++){
					int a=i+gox[k],b=j+goy[k];
					if (pd[a][b]) imp[a][b]=1;
				}
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++) impnum+=imp[i][j];
/*	for (int i=1;i<=n;i++){
		for (int j=1;j<=n;j++) cout<<(int)imp[i][j]; cout<<endl;}
	cout<<endl;
	for (int i=1;i<=n;i++){
		for (int j=1;j<=n;j++) cout<<(int)pd[i][j]; cout<<endl;}*/
	ans=allimp(); //cout<<ans<<" "<<impnum<<endl;
	getw1(); getw2();
	if (K==1){
		printf("%d\n",ans); return 0;
	}
	for (int i=0;i<x[K].size();i++) ans=(ans+matchpattern(x[K][i]))%mo; //cout<<ans<<endl;
	if (K==2){
		printf("%d\n",ans); return 0;
	}
	for (int i=0;i<x[K-1].size();i++) ans=(ans+matchwithonepoint(x[K-1][i]))%mo;// cout<<ans<<endl;
	if (K==3){
		printf("%d\n",ans); return 0;
	}
	for (int i=0;i<x[K-2].size();i++) ans=(ans+matchwithtwopoint(x[K-2][i]))%mo;// cout<<ans<<endl;
	ans=(ans+matchtwonotimp())%mo;
	printf("%d\n",ans);
	return 0;
}