1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> BI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937_64 mrand(114514); 
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

template<int MOD, int RT> struct mint {
	static const int mod = MOD;
	static constexpr mint rt() { return RT; } // primitive root for FFT
	int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int
	mint():v(0) {}
	mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD);
		if (v < 0) v += MOD; }
	bool operator==(const mint& o) const {
		return v == o.v; }
	friend bool operator!=(const mint& a, const mint& b) { 
		return !(a == b); }
	friend bool operator<(const mint& a, const mint& b) { 
		return a.v < b.v; }
   
	mint& operator+=(const mint& o) { 
		if ((v += o.v) >= MOD) v -= MOD; 
		return *this; }
	mint& operator-=(const mint& o) { 
		if ((v -= o.v) < 0) v += MOD; 
		return *this; }
	mint& operator*=(const mint& o) { 
		v = int((ll)v*o.v%MOD); return *this; }
	mint& operator/=(const mint& o) { return (*this) *= inv(o); }
	friend mint pow(mint a, ll p) {
		mint ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mint inv(const mint& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mint operator-() const { return mint(-v); }
	mint& operator++() { return *this += 1; }
	mint& operator--() { return *this -= 1; }
	friend mint operator+(mint a, const mint& b) { return a += b; }
	friend mint operator-(mint a, const mint& b) { return a -= b; }
	friend mint operator*(mint a, const mint& b) { return a *= b; }
	friend mint operator/(mint a, const mint& b) { return a /= b; }
};

const int MOD=1000000007; 
using mi = mint<MOD,5>; // 5 is primitive root for both common mods

namespace simp {
	vector<mi> fac,ifac,invn;
	void check(int x) {
		if (fac.empty()) {
			fac={mi(1),mi(1)};
			ifac={mi(1),mi(1)};
			invn={mi(0),mi(1)};
		}
		while (SZ(fac)<=x) {
			int n=SZ(fac),m=SZ(fac)*2;
			fac.resize(m);
			ifac.resize(m);
			invn.resize(m);
			for (int i=n;i<m;i++) {
				fac[i]=fac[i-1]*mi(i);
				invn[i]=mi(MOD-MOD/i)*invn[MOD%i];
				ifac[i]=ifac[i-1]*invn[i];
			}
		}
	}
	mi gfac(int x) {
		assert(x>=0);
		check(x); return fac[x];
	}
	mi ginv(int x) {
		assert(x>0);
		check(x); return invn[x];
	}
	mi gifac(int x) {
		assert(x>=0);
		check(x); return ifac[x];
	}
	mi binom(int n,int m) {
		if (m < 0 || m > n) return mi(0);
		return gfac(n)*gifac(m)*gifac(n - m);
	}
}

const ll mod2=mod*mod;
struct Hash_table {
	static const int V=3000017;
	int fst[V],nxt[V];
	int ctm,ptm[V],T;
	ll val[V];
	array<int,3> key[V];
	void init() { T=0; ctm++;}
	void add(array<int,3> st,ll v) {
		int S=(st[0]*(1ll<<40) + st[1]*(1ll<<30) + st[2])%V;
		if (S<0) S+=V;
		if (ptm[S]!=ctm) ptm[S]=ctm,fst[S]=-1;
		for (int j=fst[S];j!=-1;j=nxt[j]) if (key[j]==st) {
			val[j]+=v;
			if (val[j]>=mod2) val[j]-=mod2;
			return;
		}
		nxt[T]=fst[S],fst[S]=T,key[T]=st,val[T]=v;
		T++;
	}
};


int n,m,k;
char s[1111];
vector<int> ret;
Hash_table dp,tmp1,tmp2;
ll bi[111][111];

int main() {
	scanf("%d%d%d",&n,&m,&k);
	rep(i,0,55) {
		bi[i][0]=bi[i][i]=1;
		rep(j,1,i) bi[i][j]=(bi[i-1][j-1]+bi[i-1][j])%mod;
	}
	int M=m<<(m-1);
	rep(i,1,m+1) {
		int v;
		if (i==m) {
			v=i<<(m-1);
			ret.pb(M+v);
			ret.pb(M-v);
		}
		else {
			rep(j,0,1<<(m-i-1)) {
				v=((i-1)<<(m-1))+((2*j+1)<<(i-1));
				ret.pb(M+v);
				ret.pb(M-v);
			}
		}
	}
	ll z=0;
	rep(i,0,k) {
		scanf("%s",s);
		ll v=-1;
		rep(i,0,m) if (s[i]!=s[0]) {
			v=(i-1)<<(m-1);
			rep(j,i+1,m) if (s[j]==s[0]) {
				v|=1<<(m+i-j-1);
			}
			v|=(1<<(i-1));
			break;
		}
		if (v==-1) v=m<<(m-1);
		if (s[0]=='N') v=-v;
		z+=v+M;
	}
	printf("%d",(int)(z==M*k));
	dp.init();
	dp.add({(int)((z>>(m-1))-m*k),n-k,(int)(z%(1<<(m-1)))},1);
	rep(i,0,m-1) {
		tmp1.init();
		rep(zz,0,dp.T) {
			auto key=dp.key[zz];
			auto r=dp.val[zz]%mod;
			auto [ip,zbit,val]=key;
			rep(p1,0,n-k-zbit+1) {
				tmp1.add({ip,zbit,val+p1},r*bi[n-k-zbit][p1]);
			}
		}
		tmp2.init();
		rep(zz,0,tmp1.T) {
			auto key=tmp1.key[zz];
			auto r=tmp1.val[zz]%mod;
			auto [ip,zbit,val]=key;			
			rep(pos,0,zbit+1) {
				tmp2.add({ip+pos*i,zbit-pos,val+pos},r*bi[zbit][pos]);
			}
		}
		dp.init();
		rep(zz,0,tmp2.T) {
			auto key=tmp2.key[zz];
			auto r=tmp2.val[zz]%mod;
			auto [ip,zbit,val]=key;
			rep(neg,0,zbit+1) if ((val+neg)%2==0) {
				dp.add({ip+neg*(-i-1),zbit-neg,(val+neg)/2},r*bi[zbit][neg]);
			}
		}
	}
	rep(i,k+1,n+1) {
		mi ret=0;
		rep(zz,0,dp.T) {
			auto key=dp.key[zz];
			mi r=dp.val[zz]%mod;
			auto [ip,zbit,val]=key;
			int o=zbit-(n-i);
			if (o>=0) {
				rep(pos,0,o+1) {
					if (ip+val+pos*m+(o-pos)*(-m)==0) {
						ret+=r*bi[zbit][o]*bi[o][pos];
					}
				}
			}
		}
		ret=ret/bi[n-k][i-k];
		printf(" %d",(int)ret);
	}
	puts("");
}