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#include <bits/stdc++.h>
namespace IO {
inline char read() { static const int IN_LEN = 1000000; static char buf[IN_LEN], *s, *t; s == t ? t = (s = buf) + fread(buf, 1, IN_LEN, stdin) : 0; return s == t ? -1 : *s++; }
template <typename T> inline void read(T &x) { static char c; static bool iosig; for (c = read(), iosig = false; !isdigit(c); c = read()) { if (c == -1) return; c == '-' ? iosig = true : 0; } for (x = 0; isdigit(c); c = read()) x = x * 10 + (c ^ '0'); iosig ? x = -x : 0; }
inline void read(char &c) { while (c = read(), isspace(c) && c != -1) ; }
inline int read(char *buf) { register int s = 0; register char c; while (c = read(), isspace(c) && c != -1) ; if (c == -1) { *buf = 0; return -1; } do buf[s++] = c; while (c = read(), !isspace(c) && c != -1); buf[s] = 0; return s; }
const int OUT_LEN = 1000000;
char obuf[OUT_LEN], *oh = obuf;
inline void print(char c) { oh == obuf + OUT_LEN ? (fwrite(obuf, 1, OUT_LEN, stdout), oh = obuf) : 0; *oh++ = c; }
template <typename T> inline void print(T x) { static int buf[30], cnt; if (x == 0) { print('0'); } else { x < 0 ? (print('-'), x = -x) : 0; for (cnt = 0; x; x /= 10) buf[++cnt] = x % 10 | 48; while (cnt) print((char)buf[cnt--]); } }
inline void print(const char *s) { for (; *s; s++) print(*s); }
inline void flush() { fwrite(obuf, 1, oh - obuf, stdout); }
struct InputOutputStream { template <typename T> inline InputOutputStream &operator>>(T &x) { read(x); return *this; }
template <typename T> inline InputOutputStream &operator<<(const T &x) { print(x); return *this; }
~InputOutputStream() { flush(); } } io; }
namespace {
using IO::io; const int MOD = 1000000007; const int MAXN = 110;
#define long long long
inline int modPow(int a, int b) { register int ret = 1; for (; b; b >>= 1, a = (long)a * a % MOD) (b & 1) ? ret = (long)ret * a % MOD : 0; return ret; }
struct Task { int inv[MAXN + 1], n, m, k; int c[MAXN + 1][MAXN + 1]; int u[MAXN + 1], r[MAXN + 1]; int f[MAXN + 1][MAXN + 1]; int s[MAXN + 1];
inline void init(const int n) { inv[0] = inv[1] = 1; for (register int i = 2; i <= n; i++) inv[i] = (long)i * inv[i - 1] % MOD; inv[n] = modPow(inv[n], MOD - 2); for (register int i = n - 1; i >= 0; i--) inv[i] = inv[i + 1] * (i + 1ll) % MOD; for (register int i = 0; i <= n; i++) { c[i][0] = 1; for (register int j = 1; j <= i; j++) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD; } }
inline int interpolation(int u, int r, int n) { static int f[MAXN + 3], pre[MAXN + 3], suf[MAXN + 3]; f[0] = 0; for (register int i = 1; i <= n + 1; i++) { f[i] = (f[i - 1] + (long)modPow(i, n - r) * modPow(u - i, r - 1)) % MOD; if (u == i) return f[i]; } pre[0] = suf[n + 2] = 1; for (register int i = 1; i <= n + 1; i++) pre[i] = (long)pre[i - 1] * (u - i) % MOD; for (register int i = n + 1; i; i--) suf[i] = (long)suf[i + 1] * (u - i) % MOD; register int ret = 0; for (register int i = 1, tmp; i <= n + 1; i++) { tmp = (long)f[i] * pre[i - 1] % MOD * suf[i + 1] % MOD * inv[i - 1] % MOD * inv[n + 1 - i] % MOD; if ((n + 1 - i) % 2) tmp = MOD - tmp; ret = (ret + tmp) % MOD; } return ret; }
inline void solve() { std::string a; a.era io >> n >> m >> k; for (register int i = 1; i <= m; i++) io >> u[i]; for (register int i = 1; i <= m; i++) io >> r[i]; init(n); for (register int i = 1; i <= m; ++i) s[i] = interpolation(u[i], r[i], n); f[0][0] = 1; for (register int i = 0; i < m; i++) { for (register int j = 0; j <= n; j++) { if (f[i][j] != 0) { for (register int k = j, ex, old; k <= n; k++) { ex = k - j, old = r[i + 1] - 1 - ex; if (old < 0) break; f[i + 1][k] = (f[i + 1][k] + (long)c[j][old] * c[n - j - 1][ex] % MOD * s[i + 1] % MOD * f[i][j] % MOD) % MOD; } } } } io << f[m][n - k - 1]; } } task;
#undef long }
int main() { task.solve(); return 0; }
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