#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
struct custom_hash
{
template<class T>
unsigned long long operator()(T v) const
{
unsigned long long x = v;
x += FIXED_RANDOM; x += 11400714819323198485ull;
x = (x ^ (x >> 30)) * 13787848793156543929ull;
x = (x ^ (x >> 27)) * 10723151780598845931ull;
return x ^ (x >> 31);
}
};
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;
template<class T>
void readi(T &x)
{
x = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
x = x * 10 + (c - '0');
c = getchar();
}
if (negative)
{
x = -x;
}
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int buf[20], n = 0;
while(output)
{
buf[n] = ((output % 10));
output /= 10;
n++;
}
for (n--; n >= 0; n--)
{
putchar(buf[n] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
return (b ? gcd(b, a % b) : a);
}
template<class T>
T randomize(T mod)
{
return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << x << endl;
#define SZ(x) ((int) (x.size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) x.begin(), x.end()
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 1000013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
int Q;
int N;
int pid;
int arr[MAXN], ans[MAXN];
void solve()
{
int mn = 0, mx = 0;
FORD(i, N, 0)
{
mn += min(-arr[i] * 2, -arr[i]);
mx += max(-arr[i] * 2, -arr[i]);
if (mx < 0)
{
ans[0] = -2;
return;
}
}
mn = 0; mx = 0;
FOR(i, 0, N)
{
mn += min(arr[i] * 2, arr[i]);
mx += max(arr[i] * 2, arr[i]);
if (mx < 0)
{
ans[0] = -2;
return;
}
}
if (mx < 0 || mn > 0)
{
ans[0] = -2;
return;
}
//otherwise i think there's a solution!
//take mx, and reduce it
FOR(i, 0, N)
{
if (arr[i] == 1)
{
ans[i] = 2;
}
if (arr[i] == -1)
{
ans[i] = 0;
}
}
bool cnt = 0;
FORD(i, N + 1, 0)
{
if (i != N)
{
if (arr[i] == 1)
{
ans[i] = cnt;
cnt ^= 1;
}
else
{
ans[i] = 2;
}
mx--;
}
if (mx == 0)
{
// cerr << "end " << i << endl;
cnt ^= 1;
//cnt is how much ONE exceeds ZERO?
FOR(j, 0, i)
{
if (arr[j] == -1)
{
ans[j] = cnt;
cnt ^= 1;
}
}
break;
}
}
}
void gen()
{
//a <= 2b <= 4a AND a <= 2b both ways
//dp[a][b][c] = TOTAL a, b is # of 1's, b is min value of 2b - a
int dp[2][303][905];
FOR(i, 0, 2)
{
FOR(j, 0, 303)
{
FOR(k, 0, 903)
{
dp[i][j][k] = 0;
}
}
}
dp[0][0][301] = 1;
FOR(i, 0, 301)
{
FOR(j, 0, i + 1)
{
FOR(k, -301, 603)
{
int a = j, b = i - j;
if (a > 2 * b || dp[0][j][301 + k] == 0) continue;
//add a )
dp[1][j + 1][301 + min(k + 2, 2)] += dp[0][j][301 + k]; nmod(dp[1][j + 1][301 + min(k + 2, 2)], INF);
//add a (
dp[1][j][301 + min(k - 1, -1)] += dp[0][j][301 + k]; nmod(dp[1][j][301 + min(k - 1, -1)], INF);
if (a <= 2*b && 2*b <= 4*a && k >= 0)
{
ans[i] += dp[0][j][301 + k]; nmod(ans[i], INF);
}
}
}
FOR(j, 0, 303)
{
FOR(k, 0, 905)
{
dp[0][j][k] = dp[1][j][k]; dp[1][j][k] = 0;
}
}
}
}
int32_t main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
// freopen ("file.in", "r", stdin);
// freopen ("file.out", "w", stdout);
cin >> pid >> Q;
if (pid == 1)
{
// cerr << endl;
while(Q--)
{
string temps;
cin >> temps; N = SZ(temps);
FOR(j, 0, N)
{
arr[j] = (temps[j] == '(' ? 1 : -1);
}
solve();
if (ans[0] == -2)
{
cout << "impossible\n";
continue;
}
FOR(j, 0, N)
{
if (ans[j] == 0) cout << 'B';
if (ans[j] == 1) cout << 'R';
if (ans[j] == 2) cout << 'G';
}
cout << '\n';
}
}
if (pid == 2)
{
gen();
while(Q--)
{
cin >> N;
cout << ans[N] << '\n';
}
}
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
