Problem: Whoso in ignorance draws near to them and hears the Sirens' voice, he nevermore returns.

Homer, Odyssey

In the times of Jason and the Argonauts, it was well known that sirens use the sound of their songs to lure sailors into their demise. Yet only a few knew that every time sirens call a sailor by his name, his will weakens, making him more vulnerable. 

For the purpose of this problem, both siren songs and names of the sailors will be represented as strings of lowercase English letters. The more times the sailor's name occurs as a contiguous substring of the song, the greater danger he is in.

Jason found out that sirens can sing one of the n+1 songs, which have the following structure: let s_i (0 ≤ i ≤ n) be the i-th song and t be a string of length n, then for every i < n: s_{i+1} = s_i t_i s_i. In other words i+1-st song is the concatenation of i-th song, i-th letter (0-indexed) of t and the i-th song. 

Fortunately, he also knows s_0 and t. Jason wonders how many times a sailor's name is mentioned in a particular song. Answer q queries: given the sailor's name (w) and the index of a song (i) output the number of occurrences of w in s_i as a substring. As this number can be quite large, output its remainder modulo 10^9+7.

Input

In the first line of input there are two integers n, q (  1 ≤ n, q ≤ 10^5) meaning that there are n+1 songs and q queries. In the next two lines strings s_0 and t follow (1 ≤ |s_0| ≤ 100, |t| = n). 

Next q lines describe the queries; each one contains an integer k ( 0 ≤ k ≤ n), the index of the song sung by the sirens, and a non-empty string w, which is the name of a sailor. All strings in this problem consist only of lowercase English letters, and the sum of lengths of sailors' names does not exceed 10^6.

Output

Output q lines, i-th of them should contain the remainder modulo 10^9+7 of the number of occurrences of w in s_k.

Examples

Input


3 3
aa
bcd
2 aba
3 ca
3 aa


Output


2
2
8


Input


4 5
aba
bbac
1 a
3 baca
3 ab
2 bab
4 aba


Output


4
0
14
6
28

Note

In the first example songs of the sirens are as follows: 

  * Song 0: aa
  * Song 1: aabaa
  * Song 2: aabaacaabaa
  * Song 3: aabaacaabaadaabaacaabaa

Solution (in CPP):

Solution:
#pragma GCC optimize ("O3", "unroll-loops")
//#pragma GCC target ("avx2")
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include "bits/stdc++.h"
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define distinct(x) sort(all(x)); x.resize(unique(all(x))-x.begin())
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define CASE(x) int x; cin >> x; while (x--)
#define CASEt(x) int x; cin >> x; for (int tc = 1; tc <= x; ++tc)
using namespace std;
namespace {
	const int MOD107 = 1000000007;
	const int MOD998 = 998244353;
	using ll = long long;
	using ull = unsigned long long;
	using pii = pair<int, int>;
	using pll = pair<ll, ll>;
	template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
	template <class T> using maxheap = priority_queue<T, vector<T>, less<T>>;
	mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//	mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
	struct Modular {
	private:
		long long MODVALUE = 0;
		long long val = 0;

		Modular initModular(long long val) const { return Modular(val, MODVALUE); }

	#ifdef LOCAL
		inline void validate() const {
			assert(MODVALUE != 0);
		}

		inline void validate(const Modular& other) const {
			assert(MODVALUE != 0);
			assert(MODVALUE == other.MODVALUE);
			other.validate();
		}
	#else
		inline void validate() const { }
		inline void validate(const Modular& other) const { }
	#endif

	public:
		explicit operator long long() const { return val; }

		template<class T> Modular& operator = (const T& other) { val = other; return *this; }
		template<class T> void setMod(const T& MOD) { MODVALUE = MOD; }

		Modular& operator += (const Modular& other) { validate(other); val += other.val; val %= MODVALUE; return *this; }
		Modular  operator +  (const Modular& other) const { Modular tmp = *this; return tmp += other; }
		template<class T> Modular& operator += (const T& other) { return *this += initModular(other); }
		template<class T> Modular  operator +  (const T& other) const { return *this +  initModular(other); }
		template<class T> friend Modular operator + (const T& other, const Modular& m) { return m.initModular(other) + m; }

		Modular& operator ++()    { return *this += 1; }
		Modular  operator ++(int) { Modular tmp = *this; ++*this; return tmp; }

		Modular  operator -  () const { return initModular(-val); }
		Modular& operator -= (const Modular& other) { validate(other); val -= other.val; val += MODVALUE; val %= MODVALUE; return *this;}
		Modular  operator -  (const Modular& other) const { Modular tmp = *this; return tmp -= other; }
		template<class T> Modular& operator -= (const T& other) { return *this -= initModular(other); }
		template<class T> Modular  operator -  (const T& other) const { return *this -  initModular(other); }
		template<class T> friend Modular operator - (const T& other, const Modular& m) { return m.initModular(other) - m; }

		Modular& operator --()    { return *this -= 1; }
		Modular  operator --(int) { Modular tmp = *this; --*this; return tmp; }

		Modular& operator *= (const Modular& other) { validate(other); val *= other.val; val %= MODVALUE; val += MODVALUE; val %= MODVALUE; return *this; }
		Modular  operator *  (const Modular& other) const { Modular tmp = *this; return tmp *= other; }
		template<class T> Modular& operator *= (const T& other) { return *this *= initModular(other); }
		template<class T> Modular  operator *  (const T& other) const { return *this *  initModular(other); }
		template<class T> friend Modular operator * (const T& other, const Modular& m) { return m.initModular(other) * m; }

		Modular pow(long long power) const {
			Modular m = *this, ans = initModular(1);
			while (power) {
				if (power & 1) ans *= m;
				m *= m;
				power >>= 1;
			}
			return ans;
		}
		Modular pow(const Modular& other) const { return pow(other.val); }
		Modular inv() const { return pow(MODVALUE - 2); }

		Modular& operator /= (const Modular& other) { val *= other.inv().val; val %= MODVALUE; return *this; }
		Modular  operator /  (const Modular& other) const { Modular tmp = *this; return tmp /= other; }
		template<class T> Modular& operator /= (const T& other) { return *this /= initModular(other); }
		template<class T> Modular  operator /  (const T& other) const { return *this /  initModular(other); }
		template<class T> friend Modular operator / (const T& other, const Modular& m) { return m.initModular(other) / m; }

		friend istream& operator >> (istream& in, Modular& m) { in >> m.val; m.val %= m.MODVALUE; m.val += m.MODVALUE; m.val %= m.MODVALUE; return in; }
		friend ostream& operator << (ostream& out, const Modular& m) { return out << m.val; }

		Modular() { val = 0; MODVALUE = 0; }
		Modular(long long val, long long MOD) : MODVALUE(MOD), val((val % MOD + MOD) % MOD) { }
	};
	using Mint = Modular;
	inline ll binpow(ll b, ll p, ll mod) {
		b %= mod;
		ll ans = 1;
		for (; p > 0; p >>= 1) {
			if (p&1) {ans *= b; ans %= mod;}
			b *= b;
			b %= mod;
		}
		return ans;
	}
	inline ll max(ll a, int b) { return (a > b ? a : b); }
	inline ll max(int a, ll b) { return (a > b ? a : b); }
	inline ll min(ll a, int b) { return (a < b ? a : b); }
	inline ll min(int a, ll b) { return (a < b ? a : b); }
	template <class T> inline bool chkmin(T&x, const T& y) { return x > y ? x = y, 1 : 0; }
	template <class T> inline bool chkmax(T&x, const T& y) { return x < y ? x = y, 1 : 0; }
}
namespace IO {
	template<class T> inline void _R(T &x) {cin >> x;}
	template<class T1, class T2> inline void _R(pair<T1,T2> &x) {_R(x.first); _R(x.second);}
	template<class T> inline void _R(vector<T> &x) {for (auto& i : x) _R(i);}
	template<class T> inline void _R(deque<T> &x) {for (auto& i : x) _R(i);}
	inline void R() {}
	template<class T1, class... T2> inline void R(T1 &x, T2 &...y) { _R(x); R(y...);}

	template<class T> inline void _W(const T& x);
	template<class T1, class T2> inline void _W(const pair<T1,T2>& p);
	template<class... T> inline void _W(const vector<T...>& x);
	template<class... T> inline void _W(const deque<T...>& x);
	template<class... T> inline void _W(const forward_list<T...>& x);
	template<class... T> inline void _W(const list<T...>& x);
	template<class... T> inline void _W(const set<T...>& x);
	template<class... T> inline void _W(const multiset<T...>& x);
	template<class... T> inline void _W(const unordered_set<T...>& x);
	template<class... T> inline void _W(const unordered_multiset<T...>& x);
	template<class... T> inline void _W(const map<T...>& x);
	template<class... T> inline void _W(const multimap<T...>& x);
	template<class... T> inline void _W(const unordered_map<T...>& x);
	template<class... T> inline void _W(const unordered_multimap<T...>& x);

	template<class Container> inline void printContainer(const Container& x) { bool isFirst = 1; for (auto i : x) { if (!isFirst) cout << ' '; isFirst = 0; _W(i); } }

	template<class T> inline void _W(const T& x) {cout << x;}
	template<class T1, class T2> inline void _W(const pair<T1,T2>& p) {_W(p.first); _W(' '); _W(p.second);}
	template<class... T> inline void _W(const vector<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const deque<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const forward_list<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const list<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const set<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const multiset<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const unordered_set<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const unordered_multiset<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const map<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const multimap<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const unordered_map<T...>& x) { printContainer(x); }
	template<class... T> inline void _W(const unordered_multimap<T...>& x) { printContainer(x); }

 	inline void W() {cout << '\n';}
	template<class T> inline void W(const T &x) {_W(x); W();}
	template<class T1, class... T2> inline void W(const T1 &x, const T2 &...y) { _W(x); _W(' '); W(y...);}
} using namespace IO;
namespace outputFormat{
	inline string Case(int tc) {return "Case #" + to_string(tc) + ':';}
	inline string YN(bool b) {return b ? "Yes" : "No";}
} using namespace outputFormat;
namespace std {
    template <class T1, class T2> struct hash<pair<T1,T2>> {
    	std::size_t operator()(pair<T1,T2> _) const {
        	return hash<T1>{}(_.first) ^ hash<T2>{}(_.second);
    	}
    };
}
const Mint ZERO = Mint(0, MOD998);

struct KMP {
	vector<int> next;
	string s;

	inline int match(string& t) {
		int ans = 0;
		for (int i = 0, j = -1; i < (int)t.length(); i++) {
			while (j >= 0 && s[j + 1] != t[i]) j = next[j];
			if (s[j + 1] == t[i]) j++;
			if (j == s.length()-1) {
				ans++;
				j = next[j];
			}
		}
		return ans;
	}

	inline KMP(string& s) : s(s) {
		next.resize(s.length());
		next[0] = -1;
		for (int i = 1; i < (int)s.length(); i++) {
			int j = next[i - 1];
			while (j >= 0 && s[j + 1] != s[i]) j = next[j];
			if (s[j + 1] == s[i]) j++;
			next[i] = j;
		}
	}
};

int main() {
	int n,q; R(n,q);
	vector<string> s(1); R(s[0]);
	string t; R(t);

	const unsigned int MAXL = 1000000;
	for (int i = 0; s.back().length() < MAXL; i++)
		s.emplace_back(s.back() + t[i] + s.back());

	const Mint TWO = Mint(2, MOD107);
	const Mint TWOinv = TWO.inv();

	vector<vector<Mint>> occv(26, vector<Mint>(n + 1, Mint(0, MOD107)));
	{
		Mint now = Mint(1, MOD107);
		for (int i = 1; i <= n; i++) {
			now *= TWOinv;
			occv[t[i - 1] - 'a'][i] += now;
		}

		for (int i = 0; i < 26; i++)
			for (int j = 1; j <= n; j++)
				occv[i][j] += occv[i][j - 1];
	}
	
	while (q--) {
		int k; R(k);
		string w; R(w);
		const int len = w.length();

		KMP kmp(w);

		int smin = 0;
		while (s[smin].length() < len) ++smin;

		if (smin > k) {
			W(0);
			continue;
		}

		int match = kmp.match(s[smin]);
		vector<Mint> occ(26, Mint(0, MOD107));
		vector<int> tmatch(26, 0);
		{
			Mint mul = TWO.pow(k);
			for (int i = 0; i < 26; i++)
				occ[i] = (occv[i][k] - occv[i][smin]) * mul;

			string toMatch = s[smin].substr(s[smin].length() - len + 1, len - 1) + '_' + s[smin].substr(0, len - 1);

			for (int i = 0; i < 26; i++) {
				toMatch[len - 1] = 'a' + i;
				tmatch[i] = kmp.match(toMatch);
			}
		}
		
		Mint ans = Mint(0, MOD107);
		ans += match * TWO.pow(k - smin);

		for (int i = 0; i < 26; i++)
			ans += tmatch[i] * occ[i];

		W(ans);
	}

	return 0;
}

static auto __init__ = [](){
#ifndef LOCAL
	ios::sync_with_stdio(false);
	// cin.tie(0);
#endif
	cout << fixed << setprecision(10);
	return 42;
}();